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A365024
Starts of runs of 3 consecutive Carmichael numbers (A002997) without a non-prime-power weak Carmichael number (A087442) between any two consecutive members.
3
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
1,1
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, List of triples.
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[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]
CROSSREFS
Subsequence of A002997 and A365023.
Sequence in context: A186614 A251279 A205941 * A287591 A308086 A216123
KEYWORD
nonn
AUTHOR
Amiram Eldar, Aug 17 2023
STATUS
approved