This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A308086 #20 Apr 21 2024 10:00:04 %S A308086 656601,11512252145095521,35151891169379601,89283676825965441, %T A308086 209606994019068801,584047819872236721,627126355430628801, %U A308086 1107574117930742001,1152431453119654401,2990125943388676401,6919232969930803761 %N A308086 Carmichael numbers c such that c-4, c-2 and c+2 are primes. %C A308086 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 A308086 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 A308086 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 A308086 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 A308086 Cf. A002997, A007530, A022004, A022005, A230715, A258801, A287591. %K A308086 nonn %O A308086 1,1 %A A308086 _Rick L. Shepherd_, May 11 2019 %E A308086 More terms from _Amiram Eldar_, Jul 02 2019