factorion {FunWithNumbers}

Find Factorion Numbers. ~~

Description

This function calculates the factorion value for the specified input integer. A number is a 'factorion' if it equals the sum of the factorials of its digits in a given base.

Usage

factorion(x, base = 10 , findcycle = FALSE, maxiter = 100)

Arguments

x

The integer, or bigz integer, or character string representing an integer.

base

The the base of the input integer x. Bases 2 through 36 are supported. Default is 10.

findcycle

Logical value indicating whether or not to test for cyclic values. See Details for more information.

maxiter

A "safety switch" to avoid possible infinite loops, terminating the function prior to convergence. Only applicable when findcycle is TRUE.

Details

Most numbers are neither factorion nor part of a factorion cycle. A cycle occurs if the sequence factorion(factorion(...factorion(x))) repeats.

Value

A list containing: x echoing back the input argument. isfactorion value 1 if x is a factorion and 0 otherwise. theseq the sequence of values as each output is fed back to the input.

Author(s)

Carl Witthoft, [e-mail]

References

https://en.wikipedia.org/wiki/Factorion https://oeis.org/A014080

Examples

(factorion(3,base=8,findcycle= TRUE))
# 3   6   1320   12; isit = 0
(factorion(41, base = 6))
# isit = 1