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

656601, 5968873, 9582145, 45877861, 67653433, 84311569, 171454321, 171679561, 193708801, 193910977, 230630401, 357277921, 367804801, 393122521, 393513121, 393716701, 395044651, 557160241, 703995733, 710382401, 775368901, 832060801, 833608321, 834244501, 939947009

Offset: 1

Author

Amiram Eldar, Aug 17 2023

Keywords

• nonn

Comments

The second member in each triple is a term of both A365022 and A365023.

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.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..214
• Amiram Eldar, List of triples.
• 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 and A365023.

Cf. A000961, A087442, A225498, A365022.

Programs

Mathematica

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