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A265166 Numbers n such that 2^n-1 and 5^n-1 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 (list; graph; refs; listen; history; text; internal format)
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: A324761 A244579 A151991 * A336620 A318978 A327755

Adjacent sequences:  A265163 A265164 A265165 * A265167 A265168 A265169

KEYWORD

nonn

AUTHOR

Vincenzo Librandi, May 01 2016

STATUS

approved

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Last modified May 20 08:03 EDT 2022. Contains 353852 sequences. (Running on oeis4.)