A308086 Carmichael numbers c such that c-4, c-2 and c+2 are primes.

656601, 11512252145095521, 35151891169379601, 89283676825965441, 209606994019068801, 584047819872236721, 627126355430628801, 1107574117930742001, 1152431453119654401, 2990125943388676401, 6919232969930803761

Offset: 1

Author

Rick L. Shepherd, May 11 2019

Keywords

• nonn

Comments

Subsequence of A287591 (Carmichael numbers that are arithmetic means of cousin primes). Calculated from Amiram Eldar's table in that sequence. The Carmichael numbers here are contained within intervals defined by prime triples of the form (p, p+2, p+6); therefore, for each term, four consecutive odd numbers are prime, prime, Carmichael number (divisible by 3), then prime. None of the terms of A287591 available so far are contained within intervals defined by prime triplets of the form (p, p+4, p+6). Is that possible? If so, is it also possible for a Carmichael number to be immediately preceded and succeeded by twin primes, i.e., to be "contained" in a prime quadruplet? (Such Carmichael numbers would necessarily be multiples of 15.)

Examples

			656601 = 3*11*101*197 is a term because 656597 and 656599 are twin primes, 656601 is a Carmichael number, and 656603 is also a prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..36 (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.

Crossrefs

Cf. A002997, A007530, A022004, A022005, A230715, A258801, A287591.

Extensions

More terms from Amiram Eldar, Jul 02 2019