cp's OEIS Frontend

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.

A272754 Primes p such that p + 2 is a Carmichael number (A002997).

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%I A272754 #14 Jun 25 2019 11:51:14
%S A272754 1103,2819,6599,29339,41039,52631,62743,172079,188459,278543,340559,
%T A272754 488879,656599,670031,1033667,2100899,3146219,5048999,6049679,8719307,
%U A272754 10024559,10402559,10877579,11119103,12261059,14913989,15247619,15829631,15888311,17315999,17812079,18900971,25603199,26921087
%N A272754 Primes p such that p + 2 is a Carmichael number (A002997).
%C A272754 Because of Korselt's criterion, prime p is a member of this sequence if and only if p+2 is composite squarefree and q-1 divides p+1 for every prime q dividing p+2.
%H A272754 Amiram Eldar, <a href="/A272754/b272754.txt">Table of n, a(n) for n = 1..10000</a>
%e A272754 1103 is a term because 1103 is prime and 1105 is a Carmichael number.
%t A272754 Select[Cases[Range[1, 10^7, 2], n_ /; Mod[n, CarmichaelLambda[n]] == 1 && ! PrimeQ[n]] - 2, PrimeQ] (* _Michael De Vlieger_, May 05 2016, after _Artur Jasinski_ at A002997 *)
%o A272754 (PARI) isA002997(n) = {my(f); bittest(n, 0) && !for(i=1, #f=factor(n)~, (f[2, i]==1 && n%(f[1, i]-1)==1)||return) && #f>1}
%o A272754 lista(nn) = forprime(p=2, nn, if(isA002997(p+2), print1(p, ", ")));
%Y A272754 Cf. A002997, A135437.
%K A272754 nonn
%O A272754 1,1
%A A272754 _Altug Alkan_, May 05 2016