

A265166


Numbers n such that 2^n1 and 5^n1 are coprime.


0



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
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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. 3138.


EXAMPLE

gcd(2^11, 5^11) = gcd(1,4) = 1, so a(1) = 1.
gcd(2^31, 5^31) = gcd(7,124) = 1, so a(2) = 3.
gcd(2^41, 5^41) = 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^n1, 5^n1) eq 1];


CROSSREFS

Cf. A000225, A024049, A263647, A270390.
Sequence in context: A324761 A244579 A151991 * A336620 A318978 A327755
Adjacent sequences: A265163 A265164 A265165 * A265167 A265168 A265169


KEYWORD

nonn


AUTHOR

Vincenzo Librandi, May 01 2016


STATUS

approved



