A135437 Primes with a twin Carmichael number: primes p such that p-2 or p+2 are Carmichael numbers.

563, 1103, 2467, 2819, 6599, 29339, 41039, 52631, 62743, 172079, 188459, 278543, 340559, 488879, 656599, 656603, 670031, 1033667, 1909003, 2100899, 3146219, 5048999, 6049679, 8719307, 10024559, 10402559, 10877579, 11119103, 12261059, 14913989, 15247619

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1878 from Pierre CAMI)

Example

563 is in the sequence since it is a prime number, and 563 - 2 = 561 is a Carmichael number.
1103 is in the sequence since it is a prime number, and 1103 + 2 = 1105 is a Carmichael number.

Mathematica

s = {}; carmichaelQ[n_] := CompositeQ[n] && Divisible[n - 1, CarmichaelLambda[n]]; Do[If[carmichaelQ[n], If[PrimeQ[n - 2], AppendTo[s, n - 2]]; If[PrimeQ[n + 2], AppendTo[s, n + 2]]], {n, 10^6}]; s (* Amiram Eldar, Jul 07 2019 *)

Crossrefs

Cf. A002997, A287591.

Sequence in context: A250976 A209907 A232679 * A142759 A187849 A237029

Adjacent sequences: A135434 A135435 A135436 * A135438 A135439 A135440

Keyword

nonn

Author

Pierre CAMI, Dec 14 2007, corrected Jun 22 2008; Sep 17 2008

Status

approved