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Carmichael numbers c such that c-4, c-2 and c+2 are primes.
1

%I #20 Apr 21 2024 10:00:04

%S 656601,11512252145095521,35151891169379601,89283676825965441,

%T 209606994019068801,584047819872236721,627126355430628801,

%U 1107574117930742001,1152431453119654401,2990125943388676401,6919232969930803761

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

%C 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.)

%H Amiram Eldar, <a href="/A308086/b308086.txt">Table of n, a(n) for n = 1..36</a> (terms below 10^22, calculated using data from Claude Goutier)

%H Claude Goutier, <a href="http://www-labs.iro.umontreal.ca/~goutier/OEIS/A055553/">Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22</a>.

%e 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.

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

%K nonn

%O 1,1

%A _Rick L. Shepherd_, May 11 2019

%E More terms from _Amiram Eldar_, Jul 02 2019