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

Author

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

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A002997, A287591.

Programs

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 *)