cp's OEIS Frontend

A365024 Starts of runs of 3 consecutive Carmichael numbers (A002997) without a non-prime-power weak Carmichael number (A087442) between any two consecutive members.

%I A365024 #12 Apr 27 2025 00:45:16
%S A365024 656601,5968873,9582145,45877861,67653433,84311569,171454321,
%T A365024 171679561,193708801,193910977,230630401,357277921,367804801,
%U A365024 393122521,393513121,393716701,395044651,557160241,703995733,710382401,775368901,832060801,833608321,834244501,939947009
%N A365024 Starts of runs of 3 consecutive Carmichael numbers (A002997) without a non-prime-power weak Carmichael number (A087442) between any two consecutive members.
%C A365024 The second member in each triple is a term of both A365022 and A365023.
%C A365024 171454321 is the least start of 4 consecutive Carmichael numbers with this property, and 393122521 is the least start of 5, and also 6, consecutive Carmichael numbers with this property.
%H A365024 Amiram Eldar, <a href="/A365024/b365024.txt">Table of n, a(n) for n = 1..214</a>
%H A365024 Amiram Eldar, <a href="/A365024/a365024.txt">List of triples</a>.
%H A365024 Mauro Fiorentini, <a href="http://www.bitman.name/math/article/919">Carmichael gemelli (numeri di)</a> (in Italian).
%H A365024 Romeo Meštrović, <a href="http://arxiv.org/abs/1305.1867">Generalizations of Carmichael numbers I,</a> arXiv:1305.1867 [math.NT], 2013.
%t A365024 npwcQ[n_] := Length[(p = FactorInteger[n][[;; , 1]])] > 1 && AllTrue[p, Divisible[n - 1, # - 1] &]; (* A087442 *)
%t A365024 seq[indmax_] := Module[{carmichaels = Cases[Import["https://oeis.org/A002997/b002997.txt", "Table"], {_, _}][[;; , 2]], s1 = s2 = {}, c1, c2, i}, Do[c1 = carmichaels[[k]] + 2; c2 = carmichaels[[k + 1]] - 2; While[c1 < c2, If[npwcQ[c1], Break[]]; c1 += 2]; If[c1 == c2, AppendTo[s1, carmichaels[[k]]]; AppendTo[s2, carmichaels[[k + 1]]]], {k, 1, Min[indmax, Length[carmichaels] - 1]}]; i = Position[Rest[s1] - Most[s2], 0] // Flatten; s1[[i]]]; seq[200]
%Y A365024 Subsequence of A002997 and A365023.
%Y A365024 Cf. A000961, A087442, A225498, A365022.
%K A365024 nonn
%O A365024 1,1
%A A365024 _Amiram Eldar_, Aug 17 2023