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

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..61.

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.

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000225, A024049, A263647, A270390.

Sequence in context: A244579 A151991 A360114 * A366251 A336620 A318978

Adjacent sequences: A265163 A265164 A265165 * A265167 A265168 A265169

Keyword

nonn

Author

Vincenzo Librandi, May 01 2016

Status

approved