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 A294113 #21 Mar 14 2018 03:54:39
%S A294113 0,3,4,4,8,6,11,8,13,20,28,24,32,25,32,41,51,42,51,40,49,60,72,60,72,
%T A294113 84,97,111,125,109,124,107,121,136,152,169,188,169,187,206,226,204,
%U A294113 224,199,218,238,258,229,248,268,289,312,336,306,331,357,384,412
%N A294113 Sum of the smaller parts of the partitions of 2n into two parts with larger part prime.
%H A294113 Robert Israel, <a href="/A294113/b294113.txt">Table of n, a(n) for n = 1..10000</a>
%H A294113 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A294113 a(n) = Sum_{i=1..n} i * A010051(2n-i).
%F A294113 a(n) = 2*n*(A000720(2*n)-A000720(n-1)) - A034387(2*n) + A034387(n-1) for n >= 2. - _Robert Israel_, Mar 13 2018
%e A294113 For n=7, 2n = 14 can be partitioned into two parts with the larger part prime as 13 + 1, 11 + 3, and 7 + 7. So a(7) = 1 + 3 + 7 = 11. - _Michael B. Porter_, Mar 14 2018
%p A294113 N:= 1000: # to get a(1)..a(n)
%p A294113 P:= select(isprime, [2,seq(i,i=3..2*N,2)]):
%p A294113 S:= ListTools:-PartialSums(P):
%p A294113 f:= proc(n) local k1,k2;
%p A294113 k1:= numtheory:-pi(2*n);
%p A294113 k2:= numtheory:-pi(n-1);
%p A294113 2*n*(k1-k2) - S[k1] + S[k2]
%p A294113 end proc:
%p A294113 f(1):= 0:
%p A294113 seq(f(n),n=1..N); # _Robert Israel_, Mar 13 2018
%t A294113 Table[Sum[i (PrimePi[2 n - i] - PrimePi[2 n - i - 1]), {i, n}], {n, 80}]
%o A294113 (PARI) a(n) = sum(k=1, n, k*isprime(2*n-k)); \\ _Michel Marcus_, Oct 24 2017
%o A294113 (PARI) a(n) = my(res = 0); forprime(p = n, 2*n, res+=(2*n - p)); res \\ _David A. Corneth_, Oct 24 2017
%Y A294113 Cf. A000720, A010051, A034387, A294114.
%K A294113 nonn,easy
%O A294113 1,2
%A A294113 _Wesley Ivan Hurt_, Oct 22 2017