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Carmichael numbers k such that k-2 and k+2 are both primes.
4

%I #30 Apr 21 2024 09:59:44

%S 656601,25536531021,8829751133841,60561233400921,79934093254401,

%T 352609909731201,598438077923841,976515437206401,2122162714918401,

%U 2789066007968241,3767175573114801,7881891474971361,10740122274670881,11512252145095521,16924806963384321

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

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

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

%H Amiram Eldar, <a href="/A287591/b287591.txt">Table of n, a(n) for n = 1..282</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>.

%H R. G. E. Pinch, <a href="http://www.s369624816.websitehome.co.uk/rgep/cartable.html">Tables relating to Carmichael numbers</a>.

%H Andrzej Rotkiewicz, <a href="http://dml.cz/dmlcz/137472">On pseudoprimes having special forms and a solution of K. Szymiczek's problem</a>, Acta Mathematica Universitatis Ostraviensis, Vol. 13, No. 1 (2005), pp. 57-71.

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

%Y Cf. A002997, A057942, A272754.

%Y Subsequence of A258801.

%K nonn

%O 1,1

%A _Amiram Eldar_, May 26 2017