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Numbers k > 2 such that 3^(k-1) == 1 (mod k) and gcd(k, 2^(k-1)-1) = 1.
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%I #33 Sep 15 2018 16:09:11

%S 286,16531,24046,49051,72041,182527,192713,232726,258017,327781,

%T 442471,443713,453259,574397,625873,652879,655051,668431,705091,

%U 903631,1236031,1241143,1250833,1287091,1304446,1309111,1351601,1414639,1563151,1817743,1899451,1908397

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

%C The odd terms are "anti-Carmichael pseudoprimes (3,2)" defined as follows: numbers k > 1 such that 3^k == 3 (mod k) and gcd(k, 2^k-2) = 1. Cf. A300762 (2,3).

%C We impose k>2, since we want these to be pseudoprimes, thus composite numbers.

%t Select[Range[3, 2*10^6], PowerMod[3, #-1, #] == 1 && GCD[#, #-1 + PowerMod[2, #-1, #]] == 1 &] (* _Giovanni Resta_, Aug 18 2018 *)

%o (PARI) isok(k) = (k>2) && (Mod(3, k)^(k-1) == Mod(1, k)) && (gcd(k, 2^(k-1)-1) == 1); \\ _Michel Marcus_, Aug 18 2018

%Y Subsequence of A005935.

%Y Cf. A130433.

%K nonn

%O 1,1

%A _Thomas Ordowski_, Aug 18 2018

%E More terms from _Michel Marcus_, Aug 18 2018

%E Further terms from _Giovanni Resta_, Aug 18 2018