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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.

A355704 Indices k of partition function p where p(k) and p(k) + 2 are twin primes.

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%I A355704 #20 Jul 26 2022 01:34:30
%S A355704 3,4,6,13,2335166
%N A355704 Indices k of partition function p where p(k) and p(k) + 2 are twin primes.
%C A355704 Because asymptotically size of partitions number function p(n) ~ O(exp(sqrt(n))), and probability of primality of p(n) ~ O(1/sqrt(n)) and 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 A355704 a(6) > 10^7.
%e A355704 13 is a term because A000041(13) = 101 is prime and 103 is prime.
%o A355704 (PARI) for(n=1, 2500, if(ispseudoprime(p=numbpart(n))&&ispseudoprime(p+2), print1(n,", ")))
%Y A355704 Cf. A000041, A046063, A072213, A285086, A285087, A285088, A284594, A355705, A355706.
%K A355704 nonn,hard,more
%O A355704 1,1
%A A355704 _Serge Batalov_, Jul 14 2022