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 A285088 #13 Feb 16 2025 08:33:43 %S A285088 2,3,8,3947,43968,61681 %N A285088 Numbers n such that the number of partitions of n(n+1)/2 (=A000041(A000217(n))) is prime. %C A285088 Because asymptotically A000041(n*(n+1)/2) ~ exp(Pi*sqrt(2/3*(n*(n+1)/2))) / (4*sqrt(3)*(n*(n+1)/2)), the sum of the prime probabilities ~1/log(A000041(n*(n+1)/2)) is diverging and there are no obvious restrictions on primality; therefore, this sequence may be conjectured to be infinite. %H A285088 Chris K. Caldwell, <a href="https://t5k.org/top20/page.php?id=54">Top twenty prime partition numbers</a>, The Prime Pages. %H A285088 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PartitionFunctionP.html">Partition Function P</a> %H A285088 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a> %e A285088 a(3) = 8 is in the sequence because A000041(8*9/2) = 17977 is a prime. %o A285088 (PARI) for(n=1,2000,if(ispseudoprime(numbpart(n*(n+1)/2)),print1(n,", "))) %Y A285088 Cf. A000041, A046063, A072213, A284594, A285086, A285087. %K A285088 nonn,hard,more %O A285088 1,1 %A A285088 _Serge Batalov_, Apr 09 2017