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A270390
Greatest common divisor of 2^n-1 and 5^n-1.
4
1, 3, 1, 3, 1, 63, 1, 3, 1, 33, 1, 819, 1, 3, 31, 51, 1, 3591, 1, 1353, 1, 69, 1, 819, 1, 3, 1, 87, 1, 21483, 1, 51, 1, 3, 71, 1727271, 1, 3, 79, 1353, 1, 2408301, 1, 6141, 31, 141, 1, 13923, 1, 8283, 1, 159, 1, 10773, 1, 87, 1, 177, 1, 698476779, 1, 3, 1, 32691, 1
OFFSET
1,2
COMMENTS
Ailon and Rudnick conjecture that a(n) = 1 infinitely often.
LINKS
N. Ailon and Z. Rudnick, Torsion points on curves and common divisors of a^k-1 and b^k-1, arXiv:math/0202102 [math.NT], 2002; Acta Arith. 113 (2004), no. 1, 31-38.
FORMULA
a(n) = gcd(2^n - 1, 5^n - 1).
a(n) = gcd(A000225(n), A024049(n)).
EXAMPLE
For n=3, 2^3-1 = 7 and 5^3-1 = 124, thus a(3) = gcd(7,124) = 1.
MAPLE
seq(igcd(2^n-1, 5^n-1), n=1..100);
MATHEMATICA
Table[GCD[2^n - 1, 5^n - 1], {n, 100}]
PROG
(Sage) [gcd(2^n-1, 5^n-1) for n in [1..100]]
(PARI) vector(100, n, gcd(2^n-1, 5^n-1))
CROSSREFS
KEYWORD
nonn
AUTHOR
Tom Edgar, Mar 16 2016
STATUS
approved