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.
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.
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.
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.
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.
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.
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.
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.
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.