A367319 Base-2 Fermat pseudoprimes k such that (k-1)/ord(2, k) > (m-1)/ord(2, m) for all base-2 Fermat pseudoprimes m < k, where ord(2, k) is the multiplicative order of 2 modulo k.

341, 1105, 1387, 2047, 4369, 4681, 5461, 13981, 15709, 35333, 42799, 60787, 126217, 158369, 215265, 256999, 266305, 486737, 617093, 1082401, 1398101, 2113665, 2304167, 4025905, 4188889, 4670029, 6236473, 6242685, 8388607, 13757653, 16843009, 17895697, 22369621

Offset: 1

Author

Amiram Eldar, Nov 14 2023

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..182 (terms below 2^64)
• Amiram Eldar, Table of n, a(n), (a(n)-1)/ord(2, a(n)) for n = 1..182

Crossrefs

Subsequence of A001567.

Cf. A002326, A014664, A226216, A300101, A367320.

Programs

Mathematica

pspQ[n_] := CompositeQ[n] && PowerMod[2, n - 1, n] == 1; seq[kmax_] := Module[{s = {}, r, rm = 0}, Do[If[pspQ[k], r = (k - 1)/MultiplicativeOrder[2, k]; If[r > rm, rm = r; AppendTo[s, k]]], {k, 1, kmax}]; s]; seq[10^6]

PARI

ispsp(n) = n > 1 && n % 2 && Mod(2, n)^(n-1) == 1 && !isprime(n);
lista(kmax) = {my(r, rm = 0); for(k = 1, kmax, if(ispsp(k), r = (k-1)/znorder(Mod(2, k)); if(r > rm, rm = r; print1(k, ", "))));}