A318055 - OEIS

%I #40 Mar 31 2024 00:42:45

%S 247,403,559,715,871,1027,1339,1495,1651,1807,1963,2009,2035,2119,

%T 2587,2743,2899,2993,3055,3211,3523,3649,3679,3835,3977,3991,4147,

%U 4303,4331,4453,4615,4633,4699,4771,4927,5239,5395,5617,5707,5863,5995,6019,6031,6161,6331,6487,6799,6929,6955,7081,7111

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

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

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

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

%H Amiram Eldar, <a href="/A318055/b318055.txt">Table of n, a(n) for n = 1..10000</a>

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

%t Select[Range[8000], GCD[#, 2^# - 2] == 1 && GCD[#, 3^# - 3] > 1 &] (* _Amiram Eldar_, Mar 31 2024 *)

%o (PARI) isok(k) = (gcd(k,2^k-2) == 1) && (gcd(k,3^k-3) != 1); \\ _Michel Marcus_, Aug 14 2018

%o (GAP) Filtered([1..10000],k->Gcd(k,2^k-2) = 1 and Gcd(k,3^k-3) > 1);  # _Muniru A Asiru_, Oct 07 2018

%Y Subsequence of A267999 and probably of A121707.

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

%Y Cf. A005935.

%K nonn

%O 1,1

%A _Thomas Ordowski_, Aug 14 2018

%E More terms from _Michel Marcus_, Aug 14 2018