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

1,1

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.

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]

Crossrefs

Subsequence of A002997.

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

Sequence in context: A248985 A236794 A182151 * A182085 A271580 A237063

Adjacent sequences: A365020 A365021 A365022 * A365024 A365025 A365026

Keyword

nonn

Author

Amiram Eldar, Aug 17 2023

Status

approved