OFFSET
1,2
COMMENTS
a(n) divides a(k*n) if k is odd. - Robert Israel, Nov 15 2015
Conjecture: a(2^k) = 1 for k != 1. That is to say, there is no prime p > 5 such that ord(2,p) and ord(3,p) is the same power of 2, where ord(a,p) is the multiplicative order of a modulo p. - Jianing Song, Nov 20 2021
LINKS
Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)
Carlos Rivera, Puzzle 1064. GCD(2^p+1,3^p+1), The Prime Puzzles and Problems Connection.
FORMULA
MAPLE
seq(igcd(2^n+1, 3^n+1), n=1..100); # Robert Israel, Nov 15 2015
MATHEMATICA
Table[GCD[3^n+1, 2^n+1], {n, 90}] (* Harvey P. Dale, Dec 03 2012 *)
PROG
(PARI) a(n) = gcd(3^n + 1, 2^n + 1); \\ Harry J. Smith, Mar 28 2010
(Python)
from math import gcd
def a(n): return gcd(2**n + 1, 3**n + 1)
print([a(n) for n in range(1, 84)]) # Michael S. Branicky, Nov 20 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Jan 18 2002
STATUS
approved