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 A237264 #35 Mar 06 2022 13:09:11
%S A237264 0,2,4,4,8,7,13,15,22,21,28,29,36,35,44,45,54,55,67,70,83,84,96,99,
%T A237264 116,119,135,138,154,154,170,172,187,189,208,211,231,235,259,264,285,
%U A237264 286,306,310,334,337,361,366,389,390,413,416,441,443,468,471,496,498
%N A237264 Number of partitions of 3n into 3 parts with largest part prime.
%H A237264 Wesley Ivan Hurt, <a href="/A237264/b237264.txt">Table of n, a(n) for n = 1..58</a>
%H A237264 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A237264 a(n) = Sum_{j=0..n-2} ( Sum_{i=n + 1 + floor(j/2) - floor(1/(j + 1))..n + 2(j + 1)} A010051(i) ).
%e A237264 Count the primes in the first column for a(n).
%e A237264 13 + 1 + 1
%e A237264 12 + 2 + 1
%e A237264 11 + 3 + 1
%e A237264 10 + 4 + 1
%e A237264 9 + 5 + 1
%e A237264 8 + 6 + 1
%e A237264 7 + 7 + 1
%e A237264 10 + 1 + 1 11 + 2 + 2
%e A237264 9 + 2 + 1 10 + 3 + 2
%e A237264 8 + 3 + 1 9 + 4 + 2
%e A237264 7 + 4 + 1 8 + 5 + 2
%e A237264 6 + 5 + 1 7 + 6 + 2
%e A237264 7 + 1 + 1 8 + 2 + 2 9 + 3 + 3
%e A237264 6 + 2 + 1 7 + 3 + 2 8 + 4 + 3
%e A237264 5 + 3 + 1 6 + 4 + 2 7 + 5 + 3
%e A237264 4 + 4 + 1 5 + 5 + 2 6 + 6 + 3
%e A237264 4 + 1 + 1 5 + 2 + 2 6 + 3 + 3 7 + 4 + 4
%e A237264 3 + 2 + 1 4 + 3 + 2 5 + 4 + 3 6 + 5 + 4
%e A237264 1 + 1 + 1 2 + 2 + 2 3 + 3 + 3 4 + 4 + 4 5 + 5 + 5
%e A237264 3(1) 3(2) 3(3) 3(4) 3(5) .. 3n
%e A237264 ---------------------------------------------------------------------
%e A237264 0 2 4 4 8 .. a(n)
%t A237264 Table[Sum[Sum[PrimePi[i] - PrimePi[i - 1], {i, n + Floor[j/2] + 1 - Floor[1/(j + 1)], n + 2 (j + 1)}], {j, 0, n - 2}], {n, 50}]
%t A237264 Table[Count[IntegerPartitions[3 n,{3}],_?(PrimeQ[#[[1]]]&)],{n,60}] (* _Harvey P. Dale_, Mar 06 2022 *)
%Y A237264 Cf. A010051, A019298, A236364, A236370, A236758, A236762.
%K A237264 nonn,easy
%O A237264 1,2
%A A237264 _Wesley Ivan Hurt_, Feb 10 2014