A365022 The lesser of twin Carmichael numbers: a pair of consecutive Carmichael numbers (A002997) without a non-prime-power weak Carmichael number (A087442) between them.

2465, 62745, 512461, 656601, 658801, 838201, 1033669, 2100901, 4903921, 5968873, 6049681, 8341201, 8719309, 9439201, 9582145, 9585541, 11119105, 11921001, 12261061, 15829633, 17236801, 26921089, 35571601, 36121345, 38624041, 41341321, 43286881, 43584481, 45877861

Offset

1,1

Comments

The sequence of weak Carmichael numbers is A225498. The weak Carmichael numbers that are not powers of primes (A000961) are in A087442.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

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[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]

Crossrefs

Subsequence of A002997.

Cf. A000961, A087442, A225498, A365023 (greater counterparts), A365024.

Sequence in context: A236707 A304554 A152497 * A329240 A182381 A284089

Adjacent sequences: A365019 A365020 A365021 * A365023 A365024 A365025

Keyword

nonn

Author

Amiram Eldar, Aug 17 2023

Status

approved