

A037178


Longest cycle when squaring modulo nth prime.


4



1, 1, 1, 2, 4, 2, 1, 6, 10, 3, 4, 6, 4, 6, 11, 12, 28, 4, 10, 12, 6, 12, 20, 10, 2, 20, 8, 52, 18, 3, 6, 12, 8, 22, 36, 20, 12, 54, 82, 14, 11, 12, 36, 2, 21, 30, 12, 36, 28, 18, 28, 24, 4, 100, 1, 130, 66, 36, 22, 12, 46, 9, 24, 20, 12, 39, 20, 6, 172, 28, 10, 178, 60, 10, 18
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OFFSET

1,4


COMMENTS

a(n)=1 for Fermat primes, A019434. a(n)=2 for primes in A039687. a(n)=3 for primes in A050527. Sequence A141305 gives those primes p > 3 having the longest possible cycle, (p3)/2.  T. D. Noe, Jun 24 2008


LINKS

T. D. Noe, Table of n, a(n) for n=1..10000
E. L. Blanton, Jr., S. P. Hurd and J. S. McCranie, On a digraph defined by squaring modulo n, Fibonacci Quart. 30 (Nov. 1992), 322333.


FORMULA

Let p=prime(n) and k=A000265(p1), the odd part of p1. Then a(n) = ord(2,k), that is, the smallest positive integer x such that 2^x = 1 (mod k).  T. D. Noe, Jun 24 2008


PROG

(PARI) a(n) = {ppn = prime(n)  1; k = ppn >> valuation(ppn, 2); znorder(Mod(2, k)); } \\ Michel Marcus, Nov 11 2015


CROSSREFS

Cf. A019434, A039687, A050527, A141305.
Cf. A037179, A037180.
Sequence in context: A021417 A105791 A116515 * A077748 A152753 A113973
Adjacent sequences: A037175 A037176 A037177 * A037179 A037180 A037181


KEYWORD

nonn


AUTHOR

Jud McCranie


STATUS

approved



