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

Author

Amiram Eldar, Aug 17 2023

Keywords

• nonn

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.

Crossrefs

Subsequence of A002997.

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

Programs

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]