Gerald Hillier

ID:1341
First Name:Gerald
Last Name:Hillier
Last Change:2023-12-09
Number of Files:100 (5th most prolific)
Number of Downloads:102,953 (78th most downloaded)

A004290   (details) 49/50 ENG   3 KB / 1 KB
Every integer N is a factor of an integer P consisting solely of 1's & 0's, for the smallest N the values of P are given by A004290. This program finds minimal P/N.
By Gerald Hillier. 2020-04-11

Alternating Bit Sum and Partial Sums   (details) 38 ENG   2 KB / 1 KB
A program to insert symbolics in the Sequence App to reproduce the sequence A065359 and its partial sums A005536.
By Gerald Hillier. 2017-08-10

An Interesting Irregular Sequence   (details) 38 ENG   2 KB / 1 KB
A set of programs that generate an interesting irregular sequence, a generalized meta-Fibonacci sequence a(n) with parameters s=0 and k=5. This is A228297. Also generates A27868.
By Gerald Hillier. 2017-09-20

An Interesting Irregular Sequence   (details) 49/50 ENG   2 KB / 1 KB
Generates an interesting irregular sequence, a generalized meta-Fibonacci sequence a(n) with parameters s=0 and k=5. This is A228297.
By Gerald Hillier. 2017-09-20

Applying a Function to a Matrix   (details) 39/40 ENG   2 KB / 1 KB
Applies a function to matrix entered from the input line, returning the answer in Ans. The desired function should be stored in the program FNC and takes S1 as its argument.
By Gerald Hillier. 2018-05-01

Arabic to Pseudo-Roman Representation   (details) 49/50 ENG   2 KB / 1 KB
Takes an integer as input and returns the Roman representation in Arabic numerals, using OEIS A093788. For example, given 1953, otherwise known as MCMLIII, the program returns 1000100100050111, which is the letter by letter, left to right, value of the Roman letters.
By Gerald Hillier. 2017-02-25

Bell Numbers   (details) 49/50 ENG   3 KB / 1 KB
A program that returns a list of the Bell numbers (OEIS A000110) and one that returns row 0 through n of the Bell triangle (OEIS A011971), both of which require GoferLists, along with a separate program that returns the nth Bell number.
By John Keith and Gerald Hillier. 2020-04-12

Bernoulli Numbers   (details) 49/50 48 28 ENG   10 KB / 1-2 KB
Calculates Bernoulli numbers. Both integer and real versions for returning the nth Bernoulli number or the list of Bernoulli numbers from 0 through n. On the 49, is substantially faster than the built-in IBERNOULLI command. On the 48/28, is limited to smaller numbers for integers.
By John Keith and Gerald Hillier. 2023-09-24

Binary Champernowne Constant   (details) 49/50 ENG   3 KB / 1 KB
Returns the Nth digit of the binary Champernowne constant, or the first N digits.
By Gerald Hillier. 2017-07-23

Champernowne Sequence   (details) 49/50 ENG   2 KB / 1 KB
The Champernowne sequence (OEIS A030190) is a natural number sequence concatenated in binary & split into single digits: 0,1,1,0,1,1,1,0,0......... This program returns the specified element of the series.
By Gerald Hillier. 2017-02-25

COMB Replacement   (details) 38 ENG   2 KB / 1 KB
A replacement for the COMB command that handles the A < B case without an error.
By Gerald Hillier. 2017-11-20

Convert Integer Base   (details) 49/50 ENG   5 KB / 1 KB
Converts an integer from one integer base to another. Also has a version that works with reals, a version that works with negative numbers, and a version written in System RPL.
By Gerald Hillier and John Keith. 2023-05-14

Counting Base 5 without Zero   (details) 49/50 ENG   2 KB / 1 KB
For a given integer input N, this returns the Nth integer of a base 5 number system that doesn't include zero. This is OEIS A084545.
By Gerald Hillier. 2017-09-04

Cryptologically Interesting Random Bit   (details) 49/50 ENG   3 KB / 1 KB
With no input, this program returns a cryptologically interesting 0 or 1. In System RPL.
By Gerald Hillier. 2023-09-24

DE   (details) 49/50 ENG   4 KB / 2 KB
Takes real or complex numerical input and seeks a simple symbolic representation of the number, returning the input in the variable DE.OR, error in the symbolic representation in variable DE.ER and the symbolic representation to the stack. Also accepts a list of numbers.
By Gerald Hillier. 2017-12-06

Decimal Period of 1/X in Base Y   (details) 49/50 Prime ENG   4 KB / 1-2 KB
A set of programs to calculate the Decimal Period of 1/X in Base Y or the Multiplicative Order of Y (mod X). Includes a version for the Prime as well as both a User RPL and System RPL version for the 49/50 series.
By Joseph K. Horn, Gerald Hillier, and Thomas Ritschel. 2018-01-24

Digit Reversal   (details) 38 ENG   1 KB / 1 KB
For a given natural number input, this returns the digit reversed number in Ans and variable T. This is OEIS A004086.
By Gerald Hillier. 2017-10-04

Digits Sum   (details) 49/50 ENG   4 KB / 1 KB
Calculates the sum of the digits of an integer. Includes two User RPL versions, one System RPL version, and one assembly language version.
By Juan, John Keith, Gerald Hillier and others. 2023-05-14

Exact Integer Division to Integer Base   (details) 49/50 ENG   3 KB / 1 KB
Given integers A, B, and C, this program returns A / B to base C.
By Gerald Hillier. 2018-01-24

Extended (ExMath)   (details) 49/50 ENG   44 KB / 7 KB
Extends the arithmetic capabilities of the calculator from beyond the exponent limit of E+/- 499 to E+/- 49999.
By Francisco Saenz and Gerald Hillier. 2017-10-29

Factorisation   (details) 49/50 ENG   6 KB / 3 KB
Factors integers in a method similar to that built in to the calculator, but without giving up after a certain time limit.
By Gerald Hillier. 2017-06-19

Fast GCD   (details) 49/50 ENG   2 KB / 1 KB
Calculates the GCD of two integers much faster than the built-in routine. Includes separate versions optimized for the different characteristics of the 49G and 50g.
By Gerald Hillier. 2017-10-22

Fibo49 1.0   (details) 49/50 ENG   1 KB / 1 KB
Calculates Fibonacci numbers.
By Gerald Hillier. 2002-03-16

Fibonnaci Pseudoprime and Prime Test   (details) 49/50 ENG   2 KB / 1 KB
Tests a number for primality very quickly, but can sometimes produce false positives with Fibonacci pseudoprimes. Written in System RPL.
By Gerald Hillier. 2019-02-19

Find.String 2.0   (details) 49/50 ENG   4 KB / 1 KB
Finds a specific string/command among a given list of programs in the current directory. Useful when the given string might be in a very large number of programs, for instance 30 or more. Includes both User RPL and System RPL versions.
By Gil Campart and Gerald Hillier. 2023-05-14

Finds Binary Palindrome's Position   (details) 49/50 ENG   2 KB / 1 KB
For binary integer input B, returns B's position in the sequence A057148. For example, with input 1000101010101010001 it returns 1066.
By Gerald Hillier. 2018-02-18

FNINVARS   (details) 49/50 ENG   3 KB / 1 KB
Put an object on the stack, and this program provides a list of all variables in the current directory that contain that object. Also includes a program to find a string in the variables of a directory.
By Joseph K. Horn and Gerald Hillier. 2017-10-11

FP2 1.0   (details) 49/50 ENG   5 KB / 2 KB
A library to find square roots modulo a prime integer using FP2 arithmetic.
By Gerald Hillier and B. Bock. 2006-08-28

FPTR2^ZSQRT Replacement   (details) 49/50 ENG   2 KB / 1 KB
The built in integer square root-finder function returns the integer square root of N a positive integer and TRUE/FALSE if the square of the answer is exactly N or not. Sadly the square root of larger integers is not calculated correctly. This program returns the correct value.
By Gerald Hillier. 2017-09-11

Fraction Raised to a Power   (details) 49/50 ENG   2 KB / 1 KB
Very small and fast User RPL code to raise a fraction to a power.
By Gerald Hillier. 2017-10-11

Gauss Kronrod Integration 1.0   (details) 49/50 ENG   128 KB / 2 KB
Performs integration of real functions using Gauss-Lobatto-Kronrod 4-7-13 formulas (generally faster and more accurate than the built-in integrator).
By Gerald Hillier and B. Bock. 2008-05-11

GOLO.LIB 1.0   (details) 48 ENG   4 KB / 1 KB
Calculates elements of the Golomb sequence.
By Gerald Hillier. 2006-05-14

Hill's Encryption System   (details) 39/40 ENG   2 KB / 1 KB
Implement Hill's Cypher system. The program asks for an encyphering modulus, for English perhaps 26, and size of cyphering matrices and vector, conveniently 4 to fit on the screen.
By Gerald Hillier. 2018-05-01

Hill's Encryption System   (details) 38 ENG   1 KB / 1 KB
Implements Hill's Cypher system, which is a polygraphic substitution cipher based on linear algebra.
By Gerald Hillier. 2017-03-04

Integer Cube Root of an Integer   (details) 49/50 ENG   2 KB / 1 KB
For positive integer input N, this returns the integer cube root, i.e. greatest integer cubed less than or equal to N.
By Gerald Hillier. 2017-09-08

Integer Power of Ten   (details) 49/50 ENG   2 KB / 1 KB
Returns 1 for an integer power of 10 and 0 otherwise.
By Gerald Hillier. 2018-02-20

Integer Power of Ten Test   (details) 49/50 ENG   2 KB / 1 KB
For integer input, this returns 1. for an integer power of 10 and 0. otherwise. Also lists a faster version that is dependent upon ZREV: Speedily Reverse Digits of Integer.
By Gerald Hillier. 2018-02-21

Integer Ratio to Exact Repeating Decimal   (details) 49/50 ENG   4 KB / 1 KB
Expresses any ratio of two integers as an exact decimal number, indicating which digits repeat and which digits do not repeat. Includes both a User RPL version and a faster, smaller System RPL version.
By Joseph K. Horn and Gerald Hillier. 2018-01-24

Integer Square Root   (details) 49/50 ENG   2 KB / 1 KB
For a given infinite precision integer, returns its square root as the closest integer.
By Gerald Hillier. 2017-09-06

Integers with Even Digits   (details) 49/50 ENG   2 KB / 1 KB
For a given integer input N, this returns the Nth integer composed solely of even digits. This is OEIS A014263.
By Gerald Hillier. 2017-08-27

Integers with Odd Digits   (details) 49/50 ENG   2 KB / 1 KB
For a given integer input N, this returns the Nth integer composed solely of odd digits. This is OEIS A014261.
By Gerald Hillier. 2017-08-31

ISO-Gregorian Date Conversions 3.0   (details) 49/50 48 ENG   8 KB / 1 KB
Converts Gregorian dates to ISO day-week-year format and back.
By Gerald Hillier. 2015-07-26

ISPRIME? 1.0   (details) 49/50 ENG   121 KB / 1 KB
A replacement for the ISPRIME? command on the 49g and 50g.
By Gerald Hillier and B. Bock. 2010-12-15

Jacobi 1.0   (details) 38 ENG   3 KB / 1 KB
Calculates the Jacobi symbol indicating quadratic residue nature.
By Gerald Hillier and B. Bock. 2006-08-28

Lah Numbers   (details) 49/50 ENG   1 KB / 1 KB
For integer input N, K, this program returns the corresponding Lah number. Lah numbers are coefficients expressing rising factorials in terms of falling factorials.
By Gerald Hillier. 2017-02-25

Lambert W Function   (details) 49/50 ENG   1 KB / 1 KB
Returns the value of the Lambert w function to the stack given a real number.
By Gerald Hillier. 2017-02-25

Last Digit Composite   (details) 38 Prime ENG   2 KB / 1 KB
Inserts symbolics in the Sequence App to produce the sequence of numbers having right-most digit composite. This is A262389.
By Gerald Hillier and Didier Lachieze. 2017-09-20

Last Non-Zero Digit of Factorial   (details) 49/50 ENG   2 KB / 1 KB
For input N, a natural number, this returns the Nth element where the digit is the final nonzero digit of N factorial. This is A008904.
By Gerald Hillier. 2017-09-23

Last Non-Zero Digit of Factorial   (details) 38 ENG   2 KB / 1 KB
Inserts symbolics in the Sequence App to produce the sequence of numbers that are the last non-zero digit of the factorial of that number. This is A008904.
By Gerald Hillier. 2017-09-26

Logic Binary Sequence   (details) 49/50 ENG   2 KB / 1 KB
For a given integer input N, this returns the Nth integer of a base 2 number system that doesn't include zero. This is OEIS A007931.
By Gerald Hillier. 2017-09-15

Mantissa of an Extended Real   (details) 49/50 ENG   2 KB / 1 KB
Very small and fast program to get the mantissa of an extended real.
By Gerald Hillier and others. 2017-10-11

Möbius Function   (details) 49/50 ENG   2 KB / 1 KB
Calculates the Möbius function, used in number theory, usually written as μ(n) but called MOB(n) here, is defined thus: MOB(n) = 0 if n has a squared prime factor; MOB(n) = 1 if n is a square-free positive integer with an even number of prime factors; and MOB(n) = −1 if n is a square-free positive integer with an odd number of prime factors. Includes both a User RPL version and a much faster System RPL version.
By Joseph K. Horn and Gerald Hillier. 2018-03-18

N! Never Ends In This Many Zeroes   (details) 49/50 ENG   2 KB / 1 KB
For natural number input N, this returns the Nth element of the sequence where N! never ends in this many 0's. This is A000966.
By Gerald Hillier. 2017-09-29

Nednoc   (details) 49/50 ENG   2 KB / 1 KB
Takes as input some integer produced by some PRNG and returns the number of even digits to stack level 2 and the number of odd digits to stack level one. In System RPL.
By Gerald Hillier. 2023-09-24

Neighbour Function (Dedekind Cut)   (details) 38 ENG   2 KB / 1 KB
Programs to do the neighbor function and the Dedekind cut. The neighbor function for a real number N finds the nearest number to N that the calculator can represent. The Dedekind cut returns for real input N the upper and lower nearest numbers to N that the calculator can represent.
By Gerald Hillier. 2017-09-29

Nightingale Rose   (details) 48 ENG   6 KB / 1 KB
Produces nightingale roses for lists of statistics. For the G series only.
By Gerald Hillier and B. Bock. 2006-08-28

Number of Different Digits of N!   (details) 49/50 ENG   2 KB / 1 KB
For a given integer input N, this returns the number of different digits in N!. This is OEIS A137580.
By Gerald Hillier. 2017-09-23

Number of Digits of N!   (details) 49/50 ENG   2 KB / 1 KB
For a given integer input N, this returns the number of digits in N!. This is OEIS A034886.
By Gerald Hillier. 2017-09-23

Number of Divisors of N!   (details) 39/40 ENG   2 KB / 1 KB
For a given natural number input N, this returns the number of positive divisors of N!. This is OEIS A027423. For the 40 series only.
By Gerald Hillier. 2017-10-04

Number of Divisors of N!   (details) 49/50 ENG   5 KB / 1 KB
For a given natural number input N, this returns the number of positive divisors of N!. This is OEIS A027423.
By Gerald Hillier. 2017-10-04

Numbers Composed Exclusively of Digits 2, 3, 5, 7   (details) 49/50 ENG   2 KB / 1 KB
For a given integer input N, this returns the Nth integer composed only of the digits 2, 3, 5, and 7 (only prime numbers). This is OEIS A046034.
By Gerald Hillier. 2021-07-30

NumTheory38 1.1   (details) 38 DEU   23 KB / 3 KB
Group of number theory programs for modulo powering, prime testing and factorizing of integers. Includes Rabin-Miller test and Shanks square form factorization. Full documentation in German.
By Gerald Hillier. 2015-07-26

NumTheory39   (details) 39/40 DEU   20 KB / 3 KB
Group of number theory programs for modulo powering, prime testing and factorizing of integers. Includes Rabin-Miller test and Shanks square form factorization. Full documentation in German.
By Gerald Hillier. 2003-06-30

Odd Number Triangle   (details) 49/50 ENG   2 KB / 1 KB
For a given natural number input N, this returns the Nth element of a triangle where all numbers are odd, with the leftmost digit being 2 greater than the one above it and each digit to the right being 2 greater than the one before. This is OEIS A131421.
By Gerald Hillier. 2017-10-11

OEIS A035327   (details) 49/50 ENG   2 KB / 1 KB
For integer input N > -1 this returns the Nth element in the sequence OEIS A035327. Includes two approaches at the problem, one of which requires ListExt.
By Gerald Hillier and John Keith. 2019-12-31

OEIS A10785: Repdigit Numbers (in Human Readable Form)   (details) 49/50 ENG   3 KB / 1 KB
Calculates OEIS A010785, where for natural number input N the programme returns the Nth repdigit number in human readable form, e.g. for input 19531808 the program returns {8 2170201} to be read as the figure eight repeated 2170201 times.
By Gerald Hillier. 2023-05-14

OEIS A111138   (details) 49/50 38 Prime ENG   5 KB / 1 KB
Returns the Nth element of the series OEIS A111138.
By Gerald Hillier and John Keith. 2019-07-20

OEIS A2516: Earliest Sequence with A(A(N)) = 2N   (details) 49/50 ENG   2 KB / 1 KB
Takes a real integer from the stack & returns A2516(N) to stack.
By Gerald Hillier. 2022-08-28

Palindrome 1.0   (details) 49/50 ENG   3 KB / 1 KB
Finds integer palindromes by integer reversion addition.
By Gerald Hillier. 2001-04-04

Palindrome Locator   (details) 49/50 ENG   2 KB / 1 KB
Given positive integer palindromic input N, this returns the position of the palindrome in the series of palindromes ordered naturally in the sequence A002113.
By Gerald Hillier. 2018-01-24

Palindromes in Base 10 in Natural Order   (details) 49/50 ENG   4 KB / 1 KB
For natural number entry N, this returns the Nth palindrome for the sequence A002113.
By Gerald Hillier. 2018-01-24

Palindromes with Even & Odd Number of Digits   (details) 49/50 ENG   2 KB / 1 KB
Takes positive integer input N and returns the Nth even-digited palindromic number for the sequence A056524. Takes positive integer input N and returns the Nth odd-digited palindromic number for the sequence A056525.
By Gerald Hillier. 2018-01-24

Palindromic Partition of an Integer   (details) 38 ENG   2 KB / 1 KB
For integer input on HOME screen, this program returns a palindromic partition in Ans and stored in L1.
By Gerald Hillier. 2023-12-09

Parti49 1.0   (details) 49/50 ENG   1 KB / 1 KB
For integer input produces the exact number of integer partitions.
By Gerald Hillier. 2004-05-15

Partition of Integer N in M Parts   (details) 49/50 ENG   1 KB / 1 KB
Given positive integers N and M, this program returns the number of partitions of N into at most M parts.
By Gerald Hillier. 2017-02-25

PARTN 1.0   (details) 48 ENG   2 KB / 1 KB
For integer input produces the exact number of integer partitions.
By Gerald Hillier. 2011-07-24

Per Nørgård's ∞ Sequence   (details) 49/50 ENG   2 KB / 1 KB
Calculates Per Nørgård's infinity sequence, A004718.
By Gerald Hillier. 2017-12-06

Pollard's p-1 Factorization 1.0   (details) 49/50 ENG   7 KB / 1 KB
Performs Pollard's p-1 integer factorization.
By B. Bock and Gerald Hillier. 2010-06-06

Prime Count between N^2 & (N+1)^2   (details) 39/40 ENG   2 KB / 1 KB
Inserts symbolics in the Sequence App to produce the sequence of numbers where N is the number of primes between N^2 and (N+1)^2. This is A014085.
By Gerald Hillier. 2017-09-11

Prime Power Test 1.0   (details) 49/50 ENG   3 KB / 1 KB
Tests whether an integer is a prime or a power of a prime.
By Gerald Hillier and B. Bock. 2006-08-28

Product of Digits is a Prime Sequence   (details) 49/50 ENG   2 KB / 1 KB
For a given integer input N, this returns the Nth integer of the series where the elements are all numbers in naturally ascending order whose product of digits is a prime. This is OEIS A028842.
By Gerald Hillier. 2017-09-07

Quasi Monte Carlo Halton Sequence   (details) 49/50 ENG   2 KB / 1 KB
This group of programs generates a Quasi-Monte Carlo series of D-dimension Halton sequence vectors.
By Gerald Hillier. 2017-02-25

Ramanujan Tau Function   (details) 49/50 ENG   4 KB / 1 KB
Set of three User RPL programs to compute the Ramanujan tau function (A000594) for positive integers. Requires Sum of Divisors to an Integer Power and ListExt. Also includes a standalone program written in System RPL.
By John Keith and Gerald Hillier. 2018-12-21

Repunit   (details) 49/50 ENG   2 KB / 1 KB
In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. This assembly language program generates the nth repunit very quickly.
By Gerald Hillier. 2017-07-04

Roman Hours Time   (details) 49/50 ENG   2 KB / 1 KB
Converts modern clock time input in 24-hour format with decimal parts of hours to the Roman standard (used from 263 BC on).
By Gerald Hillier. 2022-02-27

RomMat 1.0   (details) 49/50 ENG   2 KB / 1 KB
Performs arithmetic on Roman numerals.
By Gerald Hillier. 2002-03-16

RSA.LIB 4.0   (details) 49/50 ENG   5 KB / 2 KB
Implementation of RSA encryption algorithm - not as a toy, but real RSA.
By Gerald Hillier. 2001-02-09

Sequence A002516   (details) 38 ENG   1 KB / 1 KB
Generates sequence A002516, the earliest sequence with a(a(n))=2n.
By Gerald Hillier. 2017-08-02

Series Factors of Natural Numbers   (details) 49/50 ENG   1 KB / 1 KB
Given positive integer input N, returns the Nth element of the series of factors of the natural numbers, per OEIS A027750.
By Gerald Hillier. 2017-02-25

Shank's Square Form Factorisation 1.0   (details) 48 ENG   2 KB / 1 KB
Integer factorization in a reasonable time for numbers up to maximum hexadecimal value.
By B. Bock and Gerald Hillier. 2002-11-17

Smallest Prime   (details) 49/50 ENG   2 KB / 1 KB
For a given natural number input N, this returns the smallest prime number beginning with N. This is OEIS A018800.
By Gerald Hillier. 2017-10-03

Smallest Prime Beginning with N Reversed   (details) 39/40 ENG   2 KB / 1 KB
For a given natural number input N, this returns the smallest prime number beginning with N reversed. This is OEIS A110743.
By Gerald Hillier. 2017-10-04

Sum of Divisors to an Integer Power   (details) 49/50 ENG   2 KB / 1 KB
Returns the sum of the given integer to the given integer real power. For powers of 0, it returns the number of divisors.
By Gerald Hillier. 2018-04-16

Test for Binary-Palindromicity   (details) 49/50 ENG   2 KB / 1 KB
For integer decimal input N, this tests whether N in binary is palindromic. This is A178225.
By Gerald Hillier. 2018-02-27

Trailing Zeros of a Factorial   (details) 39/40 ENG   1 KB / 1 KB
Inserts symbolics in the Sequence App to produce the sequence of numbers where the nth digit is the the number of trailing zeros in n!, highest power of 5 dividing n!. This is OEIS A027868.
By Gerald Hillier. 2017-09-12

Unproven Theorem A212558   (details) 49/50 ENG   2 KB / 1 KB
Calculates sequence OEIS A212558, which is a(n) = ((n - s)^2 mod (n + s)) - ((n + s)^2 mod (n - s)), where s is the sum of the decimal digits of n, and includes a proof of it.
By Gerald Hillier. 2017-12-28

Verbal Sequence   (details) 49/50 ENG   2 KB / 1 KB
Takes integer input from the stack and returns the labelled lengths of the prodromic and periodic parts of the verbal description of the input and the descriptions of the input to the stack.
By Gerald Hillier. 2017-02-25

XdYB 1.0   (details) 48 ENG   4 KB / 1 KB
Program performs exact division of real X by real Y to real integer base B. For the G series only.
By Gerald Hillier. 2001-02-12

XdYB49 1.0   (details) 49/50 ENG   3 KB / 1 KB
Performs exact division of real X by real Y to any real base B.
By Gerald Hillier. 2001-02-14

ZREV: Speedily Reverse Digits of Integer   (details) 49/50 ENG   5 KB / 1 KB
For integer input Z this returns the reversed digits integer. It is much faster than converting to a string, SREV and converting to an object. Includes a second routine that is a bit bigger but handles some more cases.
By Gerald Hillier and David Mutter. 2018-03-14

Part of the HP Calculator Archive,
Copyright 1997-2024 Eric Rechlin.