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 A355728 #14 Jul 26 2022 01:34:46 %S A355728 2,3,4,5,1085 %N A355728 Indices k of partition function where consecutive p(k) and p(k+1) are prime. %C A355728 Because asymptotically the size of the partition number function p(n) is ~ O(exp(sqrt(n))), and the probability of primality of p(n) is ~ O(1/sqrt(n)) and the combined probability of primality of p(n) and p(n+1) 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 A355728 a(6) > 10^8. %e A355728 5 is in the sequence because A000041(5) = 7 and A000041(6) = 11 are prime. %o A355728 (PARI) for(k=1, 5000, if(ispseudoprime(numbpart(k))&&ispseudoprime(numbpart(k+1)), print1(k, ", "))) %Y A355728 Cf. A000041, A046063, A072213, A284594, A285086, A285087, A285088, A355704, A355705, A355706. %K A355728 nonn,hard,more %O A355728 1,1 %A A355728 _Serge Batalov_, Jul 15 2022