A365023 - OEIS

%I #7 Aug 24 2023 03:12:21

%S 2821,63973,530881,658801,670033,852841,1050985,2113921,4909177,

%T 6049681,6054985,8355841,8719921,9494101,9585541,9613297,11205601,

%U 11972017,12262321,15888313,17316001,26932081,35703361,36765901,38637361,41471521,43331401,43620409,45890209

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

%H Amiram Eldar, <a href="/A365023/b365023.txt">Table of n, a(n) for n = 1..1000</a>

%H Mauro Fiorentini, <a href="http://www.bitman.name/math/article/919">Carmichael gemelli (numeri di)</a> (in Italian).

%H Romeo Meštrović, <a href="http://arxiv.org/abs/1305.1867">Generalizations of Carmichael numbers I,</a> arXiv:1305.1867 [math.NT], 2013.

%t npwcQ[n_] := Length[(p = FactorInteger[n][[;; , 1]])] > 1 && AllTrue[p, Divisible[n - 1, # - 1] &]; (* A087442 *)

%t 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]

%Y Subsequence of A002997.

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

%K nonn

%O 1,1

%A _Amiram Eldar_, Aug 17 2023