A272754 Primes p such that p + 2 is a Carmichael number (A002997).

1103, 2819, 6599, 29339, 41039, 52631, 62743, 172079, 188459, 278543, 340559, 488879, 656599, 670031, 1033667, 2100899, 3146219, 5048999, 6049679, 8719307, 10024559, 10402559, 10877579, 11119103, 12261059, 14913989, 15247619, 15829631, 15888311, 17315999, 17812079, 18900971, 25603199, 26921087

Offset: 1

Author

Altug Alkan, May 05 2016

Keywords

• nonn

Comments

Because of Korselt's criterion, prime p is a member of this sequence if and only if p+2 is composite squarefree and q-1 divides p+1 for every prime q dividing p+2.

Examples

			1103 is a term because 1103 is prime and 1105 is a Carmichael number.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002997, A135437.

Programs

Mathematica

Select[Cases[Range[1, 10^7, 2], n_ /; Mod[n, CarmichaelLambda[n]] == 1 && ! PrimeQ[n]] - 2, PrimeQ] (* Michael De Vlieger, May 05 2016, after Artur Jasinski at A002997 *)

PARI

isA002997(n) = {my(f); bittest(n, 0) && !for(i=1, #f=factor(n)~, (f[2, i]==1 && n%(f[1, i]-1)==1)||return) && #f>1}
lista(nn) = forprime(p=2, nn, if(isA002997(p+2), print1(p, ", ")));