A287591 Carmichael numbers k such that k-2 and k+2 are both primes.

656601, 25536531021, 8829751133841, 60561233400921, 79934093254401, 352609909731201, 598438077923841, 976515437206401, 2122162714918401, 2789066007968241, 3767175573114801, 7881891474971361, 10740122274670881, 11512252145095521, 16924806963384321

Offset: 1

Author

Amiram Eldar, May 26 2017

Keywords

• nonn

Comments

Rotkiewicz conjectured that there are infinitely many Carmichael numbers k such that k-2 or k+2 are primes.

The terms were calculated using Pinch's tables of Carmichael numbers (see link below).

Examples

			656601 is in the sequence since it is a Carmichael number (A002997) and both 656599 and 656603 are primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..282 (terms below 10^22, calculated using data from Claude Goutier)
• Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.
• R. G. E. Pinch, Tables relating to Carmichael numbers.
• Andrzej Rotkiewicz, On pseudoprimes having special forms and a solution of K. Szymiczek's problem, Acta Mathematica Universitatis Ostraviensis, Vol. 13, No. 1 (2005), pp. 57-71.

Crossrefs

Cf. A002997, A057942, A272754.

Subsequence of A258801.