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 A285087 #20 Feb 16 2025 08:33:43
%S A285087 2,13,21,46909
%N A285087 Numbers n such that the number of partitions of n^2-1 is prime.
%C A285087 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 A285087 a(5) > 50000.
%H A285087 Chris K. Caldwell, <a href="https://t5k.org/top20/page.php?id=54">Top twenty prime partition numbers</a>, The Prime Pages.
%H A285087 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PartitionFunctionP.html">Partition Function P</a>
%H A285087 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>
%F A285087 {n: A000041(n^2-1) in A000040}.
%e A285087 13 is in the sequence because A000041(13^2-1) = 228204732751 is a prime.
%o A285087 (PARI) for(n=1,2000,if(ispseudoprime(numbpart(n^2-1)),print1(n,", ")))
%o A285087 (Python)
%o A285087 from itertools import count, islice
%o A285087 from sympy import isprime, npartitions
%o A285087 def A285087_gen(startvalue=1): # generator of terms >= startvalue
%o A285087 return filter(lambda n: isprime(npartitions(n**2-1)), count(max(startvalue,1)))
%o A285087 A285087_list = list(islice(A285087_gen(),3)) # _Chai Wah Wu_, Nov 20 2023
%Y A285087 Cf. A000041, A046063, A072213, A284594, A285086, A285088.
%K A285087 nonn,hard,more
%O A285087 1,1
%A A285087 _Serge Batalov_, Apr 09 2017