NAME
Math::NumSeq::ErdosSelfridgeClass -- classification of primes
SYNOPSIS
use Math::NumSeq::ErdosSelfridgeClass;
my $seq = Math::NumSeq::ErdosSelfridgeClass->new;
my ($i, $value) = $seq->next;DESCRIPTION
A classification of primes by Erdos and Selfridge, or 0 if composite.
0,1,1,0,1,0,1,0,0,0,1,0,2,0,0,0,1,0,2,0,0,0,1,0,0,0,0,0,2,...A prime p is classified according to the prime factors of p+1. If the maximum class among those factors is c then p has class one above that, ie. c+1.
Primes 2 and 3 are reckoned as class 1, as are any primes where p+1 has factors 2 and 3 only, p=2^x+3^y-1. For example i=11 has 11+1=12=2*2*3 so it's class 1.
The classification essentially asks how many iterations of factorizing p+1 it takes to get to down to factors 2 and 3 only. For example i=617 has 617+1=2*3*103, then 103+1=104=2*13, then 13+1=2*7. 7 is a class 1, so 13 is a class 2, 103 is class 3, and finally 617 is class 4.
FUNCTIONS
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::ErdosSelfridgeClass->new ()-
Create and return a new sequence object.
$bool = $seq->ith($value)-
Return the class number of
$value, or 0 if$valueis not a prime. $bool = $seq->pred($value)-
Return true if
$valueoccurs as a classification in the sequence, which means any integer$value >= 0.