A265166 Numbers n such that 2^n-1 and 5^n-1 are coprime.

1, 3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 31, 33, 37, 41, 43, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 97, 101, 103, 107, 109, 111, 113, 115, 121, 123, 125, 127, 129, 131, 133, 137, 139, 141, 143

Offset: 1

Author

Vincenzo Librandi, May 01 2016

Keywords

• nonn

Comments

Also numbers n such that A270390(n) = 1.

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

Examples

			gcd(2^1-1, 5^1-1) = gcd(1,4) = 1, so a(1) = 1.
gcd(2^3-1, 5^3-1) = gcd(7,124) = 1, so a(2) = 3.
gcd(2^4-1, 5^4-1) = gcd(15,624) = 3, so 4 is not in the sequence.
		

Links

• N. Ailon and Z. Rudnick, Torsion points on curves and common divisors of a^k - 1 and b^k - 1 , Acta Arith. 113 (2004), pp. 31-38.

Crossrefs

Cf. A000225, A024049, A263647, A270390.

Programs

Magma

[n: n in [1..200] | Gcd(2^n-1,5^n-1) eq 1];

Mathematica

Select[Range[200], GCD[2^# - 1, 5^# - 1] == 1 &]
Select[Range[150],CoprimeQ[2^#-1,5^#-1]&] (* Harvey P. Dale, Apr 12 2018 *)