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%I #9 Aug 24 2023 03:12:37
%S 2465,62745,512461,656601,658801,838201,1033669,2100901,4903921,
%T 5968873,6049681,8341201,8719309,9439201,9582145,9585541,11119105,
%U 11921001,12261061,15829633,17236801,26921089,35571601,36121345,38624041,41341321,43286881,43584481,45877861
%N The lesser of twin Carmichael numbers: a pair of consecutive Carmichael numbers (A002997) without a non-prime-power weak Carmichael number (A087442) between them.
%C The sequence of weak Carmichael numbers is A225498. The weak Carmichael numbers that are not powers of primes (A000961) are in A087442.
%H Amiram Eldar, <a href="/A365022/b365022.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]]]], {k, 1, Length[carmichaels] - 1}]; s]; seq[10^6]
%Y Subsequence of A002997.
%Y Cf. A000961, A087442, A225498, A365023 (greater counterparts), A365024.
%K nonn
%O 1,1
%A _Amiram Eldar_, Aug 17 2023
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