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 A355956 #18 Jul 28 2022 20:58:02 %S A355956 3,5,6,13,36,157,302,546,2502,2732,19439060 %N A355956 Index k of partition function p such that p(k) is a member of a cousin prime pair. %C A355956 Because asymptotically the size of the partition number function p(n) ~ O(exp(sqrt(n))), and the probability of primality of p(n) ~ O(1/sqrt(n)) and the combined probability of primality of p(n) and p(n)+-4 is ~ O(1/n), the sum of the prime probabilities is diverging and there are no obvious restrictions on primality; therefore this sequence may be conjectured to be infinite. %C A355956 a(12) > 4*10^7. %e A355956 5 is in the sequence because A000041(5) = 7 and 7 + 4 = 11 are cousin primes. %e A355956 13 is in the sequence because A000041(13) = 101 and 101 - 4 = 97 are cousin primes. %o A355956 (PARI) for(n=1, 10000, if(ispseudoprime(p=numbpart(n))&&(ispseudoprime(p-4)||ispseudoprime(p+4)), print1(n, ", "))) %Y A355956 Cf. A000041, A046063, A072213, A285086, A285087, A285088, A284594, A355704-A355706. %K A355956 nonn,hard,more %O A355956 1,1 %A A355956 _Serge Batalov_, Jul 21 2022