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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.

%I A367319 #14 Nov 15 2023 08:05:05
%S A367319 341,1105,1387,2047,4369,4681,5461,13981,15709,35333,42799,60787,
%T A367319 126217,158369,215265,256999,266305,486737,617093,1082401,1398101,
%U A367319 2113665,2304167,4025905,4188889,4670029,6236473,6242685,8388607,13757653,16843009,17895697,22369621
%N 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.
%H A367319 Amiram Eldar, <a href="/A367319/b367319.txt">Table of n, a(n) for n = 1..182</a> (terms below 2^64)
%H A367319 Amiram Eldar, <a href="/A367319/a367319.txt">Table of n, a(n), (a(n)-1)/ord(2, a(n)) for n = 1..182</a>
%t A367319 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]
%o A367319 (PARI) ispsp(n) = n > 1 && n % 2 && Mod(2, n)^(n-1) == 1 && !isprime(n);
%o A367319 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, ", "))));}
%Y A367319 Subsequence of A001567.
%Y A367319 Cf. A002326, A014664, A226216, A300101, A367320.
%K A367319 nonn
%O A367319 1,1
%A A367319 _Amiram Eldar_, Nov 14 2023