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

1,1

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

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]

Prog

(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, ", ")))); }

Crossrefs

Subsequence of A001567.

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

Sequence in context: A271221 A066488 A291601 * A083876 A348258 A068216

Adjacent sequences: A367316 A367317 A367318 * A367320 A367321 A367322

Keyword

nonn

Author

Amiram Eldar, Nov 14 2023

Status

approved