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A263647 Numbers n such that 2^n-1 and 3^n-1 are coprime. 3
1, 2, 3, 5, 7, 9, 13, 14, 15, 17, 19, 21, 25, 26, 27, 29, 31, 34, 37, 38, 39, 41, 45, 47, 49, 51, 53, 57, 59, 61, 62, 63, 65, 67, 71, 73, 74, 79, 81, 85, 87, 89, 91, 93, 94, 97, 98, 101, 103, 107, 109, 111, 113, 118, 122, 123, 125, 127, 133, 134, 135, 137, 139, 141, 142, 145, 147, 149, 151, 153, 157, 158, 159, 163, 167, 169, 171 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

n such that there is no k for which both A014664(k) and A062117(k) divide n.

If n is in the sequence, then so is every divisor of n.

1 and 2 are the only members that are in A006093.

Conjectured to be infinite: see the Ailon and Rudnick paper.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

N. Ailon and Z. Rudnick, Torsion points on curves and common divisors of a^k - 1 and b^k - 1, Acta Arith. 113 (2004), 31-38. Also arXiv:math/0202102 [math.NT], 2002.

EXAMPLE

gcd(2^1-1, 3^1-1) = gcd(1,2) = 1, so a(1) = 1.

gcd(2^2-1, 3^2-1) = gcd(3,8) = 1, so a(2) = 2.

gcd(2^4-1, 3^4-1) = gcd(15,80) = 5, so 4 is not in the sequence.

MAPLE

select(n -> igcd(2^n-1, 3^n-1)=1, [$1..1000]);

MATHEMATICA

Select[Range[200], GCD[2^# - 1, 3^# - 1] == 1 &] (* Vincenzo Librandi, May 01 2016 *)

PROG

(MAGMA) [n: n in [1..200] | Gcd(2^n-1, 3^n-1) eq 1]; // Vincenzo Librandi, May 01 2016

CROSSREFS

Cf. A000225, A006093, A024023, A014664, A062117.

Sequence in context: A237826 A080000 A032459 * A028870 A057886 A302835

Adjacent sequences:  A263644 A263645 A263646 * A263648 A263649 A263650

KEYWORD

nonn

AUTHOR

Robert Israel, Oct 22 2015

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)