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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.

A285086 Numbers n such that the number of partitions of n^2+1 (=A000041(n^2+1)) is prime.

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%I A285086 #10 Feb 16 2025 08:33:43
%S A285086 1,2,3914
%N A285086 Numbers n such that the number of partitions of n^2+1 (=A000041(n^2+1)) is prime.
%C A285086 Because asymptotically A000041(n^2+1) ~ exp(Pi*sqrt(2/3*(n^2+1))) / (4*sqrt(3)*(n^2+1)), the sum of the prime probabilities ~ 1/log(A000041(n^2+1)) is diverging and there are no obvious restrictions on primality; therefore, this sequence may be conjectured to be infinite.
%C A285086 a(4) > 90000.
%H A285086 Chris K. Caldwell, <a href="https://t5k.org/top20/page.php?id=54">Top twenty prime partition numbers</a>, The Prime Pages.
%H A285086 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PartitionFunctionP.html">Partition Function P</a>
%H A285086 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>
%e A285086 a(2) = 2 is in the sequence because A000041(2^2+1) = 7 is a prime.
%o A285086 (PARI) for(n=1,3920,if(ispseudoprime(numbpart(n^2+1)),print1(n,", ")))
%Y A285086 Cf. A000041, A046063, A072213, A284594, A285087, A285088.
%K A285086 nonn,hard,more,bref
%O A285086 1,2
%A A285086 _Serge Batalov_, Apr 09 2017