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 A355706 #25 Jul 26 2022 01:34:40 %S A355706 3,4,5,6,13,186,3542,2335166 %N A355706 Indices k of partition function p where p(k) is a twin prime. %C A355706 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)+-2 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 A355706 p(2335166), a 1696-digit number, was known to be prime and proven prime by F. Morain using his software (ca. April 2001), but the primality of p(2335166)+2 was found by targeted search (for this sequence) in July 2022. %C A355706 a(9) > 10^7. %e A355706 13 is a term because A000041(13) = 101 is prime and 101 and 103 are twin primes. %o A355706 (PARI) for(n=1, 3600, if(ispseudoprime(p=numbpart(n))&&(ispseudoprime(p-2)||ispseudoprime(p+2)), print1(n, ", "))) %Y A355706 Subsequence of A046063. %Y A355706 Union of A355704 and A355705. %Y A355706 Cf. A000041, A072213, A285086, A285087, A285088, A284594. %K A355706 nonn,hard,more %O A355706 1,1 %A A355706 _Serge Batalov_, Jul 15 2022