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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
For integer input N, K, this program returns the corresponding Lah number. Lah numbers are coefficients expressing rising factorials in terms of falling factorials.
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.
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.
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.
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.
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.
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.
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.
Given positive integer palindromic input N, this returns the position of the palindrome in the series of palindromes ordered naturally in the sequence A002113.
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.
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.
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.
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.
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.
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.
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.
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.