A318055 Numbers k such that gcd(k, 2^k - 2) = 1 and gcd(k, 3^k - 3) > 1.

247, 403, 559, 715, 871, 1027, 1339, 1495, 1651, 1807, 1963, 2009, 2035, 2119, 2587, 2743, 2899, 2993, 3055, 3211, 3523, 3649, 3679, 3835, 3977, 3991, 4147, 4303, 4331, 4453, 4615, 4633, 4699, 4771, 4927, 5239, 5395, 5617, 5707, 5863, 5995, 6019, 6031, 6161, 6331, 6487, 6799, 6929, 6955, 7081, 7111

Offset: 1

Author

Thomas Ordowski, Aug 14 2018

Keywords

• nonn

Comments

Odd numbers k such that gcd(k,2^(k-1)-1) = 1 and gcd(k,3^(k-1)-1) > 1.

It seems that a(n) == 91 (mod 156) for infinitely many n.

Fermat pseudoprimes to base 3 (A005935) in this sequence are 16531, 49051, 72041, ...

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A267999 and probably of A121707.

Cf. A139613(2n+1): it gives many terms of the sequence.

Cf. A005935.

Programs

GAP

Filtered([1..10000],k->Gcd(k,2^k-2) = 1 and Gcd(k,3^k-3) > 1);  # Muniru A Asiru, Oct 07 2018

Maple

select(k->gcd(k,2^k-2) = 1 and gcd(k,3^k-3) > 1,[$1..10000]); # Muniru A Asiru, Oct 07 2018

Mathematica

Select[Range[8000], GCD[#, 2^# - 2] == 1 && GCD[#, 3^# - 3] > 1 &] (* Amiram Eldar, Mar 31 2024 *)

PARI

isok(k) = (gcd(k,2^k-2) == 1) && (gcd(k,3^k-3) != 1); \\ Michel Marcus, Aug 14 2018

Extensions

More terms from Michel Marcus, Aug 14 2018