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

%I A265166 #26 Sep 08 2022 08:46:14
%S A265166 1,3,5,7,9,11,13,17,19,21,23,25,27,29,31,33,37,41,43,47,49,51,53,55,
%T A265166 57,59,61,63,65,67,69,71,73,77,79,81,83,85,87,89,91,93,97,101,103,107,
%U A265166 109,111,113,115,121,123,125,127,129,131,133,137,139,141,143
%N A265166 Numbers n such that 2^n-1 and 5^n-1 are coprime.
%C A265166 Also numbers n such that A270390(n) = 1.
%C A265166 Conjectured to be infinite: see the Ailon and Rudnick paper.
%H A265166 N. Ailon and Z. Rudnick, <a href="http://arxiv.org/abs/math/0202102">Torsion points on curves and common divisors of a^k - 1 and b^k - 1 </a>, Acta Arith. 113 (2004), pp. 31-38.
%e A265166 gcd(2^1-1, 5^1-1) = gcd(1,4) = 1, so a(1) = 1.
%e A265166 gcd(2^3-1, 5^3-1) = gcd(7,124) = 1, so a(2) = 3.
%e A265166 gcd(2^4-1, 5^4-1) = gcd(15,624) = 3, so 4 is not in the sequence.
%t A265166 Select[Range[200], GCD[2^# - 1, 5^# - 1] == 1 &]
%t A265166 Select[Range[150],CoprimeQ[2^#-1,5^#-1]&] (* _Harvey P. Dale_, Apr 12 2018 *)
%o A265166 (Magma) [n: n in [1..200] | Gcd(2^n-1,5^n-1) eq 1];
%Y A265166 Cf. A000225, A024049, A263647, A270390.
%K A265166 nonn
%O A265166 1,2
%A A265166 _Vincenzo Librandi_, May 01 2016