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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.

A355705 Indices k of partition function p where p(k) and p(k) - 2 are twin primes.

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%I A355705 #17 Jul 26 2022 01:34:35
%S A355705 4,5,186,3542
%N A355705 Indices k of partition function p where p(k) and p(k) - 2 are twin primes.
%C A355705 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 A355705 a(5) > 10^7.
%e A355705 4 is a term because A000041(4) = 5, and 3 and 5 are twin primes.
%e A355705 5 is a term because A000041(5) = 7, and 5 and 7 are twin primes.
%o A355705 (PARI) for(n=1, 3600, if(ispseudoprime(p=numbpart(n))&&ispseudoprime(p-2), print1(n, ", ")))
%Y A355705 Cf. A000041, A046063, A072213, A285086, A285087, A285088, A284594, A355704, A355706.
%K A355705 nonn,hard,more
%O A355705 1,1
%A A355705 _Serge Batalov_, Jul 15 2022