A365023 The greater of twin Carmichael numbers: a pair of consecutive Carmichael numbers (A002997) without a non-prime-power weak Carmichael number (A087442) between them.

2821, 63973, 530881, 658801, 670033, 852841, 1050985, 2113921, 4909177, 6049681, 6054985, 8355841, 8719921, 9494101, 9585541, 9613297, 11205601, 11972017, 12262321, 15888313, 17316001, 26932081, 35703361, 36765901, 38637361, 41471521, 43331401, 43620409, 45890209

Offset: 1

Author

Amiram Eldar, Aug 17 2023

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000
• Mauro Fiorentini, Carmichael gemelli (numeri di) (in Italian).
• Romeo Meštrović, Generalizations of Carmichael numbers I, arXiv:1305.1867 [math.NT], 2013.

Crossrefs

Subsequence of A002997.

Cf. A000961, A087442, A225498, A365022 (lesser counterparts), A365024.

Programs

Mathematica

npwcQ[n_] := Length[(p = FactorInteger[n][[;; , 1]])] > 1 && AllTrue[p, Divisible[n - 1, # - 1] &]; (* A087442 *)
seq[nmax_] := Module[{carmichaels = Select[Range[1, nmax, 2], CompositeQ[#] && Divisible[# - 1, CarmichaelLambda[#]] &], s = {}, c1, c2}, Do[c1 = carmichaels[[k]] + 2; c2 = carmichaels[[k + 1]] - 2; While[c1 < c2, If[npwcQ[c1], Break[]]; c1 += 2]; If[c1 == c2, AppendTo[s, carmichaels[[k+1]]]], {k, 1, Length[carmichaels] - 1}]; s]; seq[10^6]