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 A116911 #11 Jan 28 2020 12:39:10
%S A116911 5,17,4957,129277,2826443,3861083,5126483,9451573,19811083,53751743,
%T A116911 68136617,98729003,264616831,388771421,498157871,608312141,682548511,
%U A116911 779346653,918754301,1174179079,1700023891,2056298683,2149703411
%N A116911 Prime partial sums of pentagonal numbers with prime indices.
%C A116911 See also: A116994 Prime partial sums of triangular numbers with prime indices. A116995 Pentagonal numbers with prime indices.
%H A116911 Harvey P. Dale, <a href="/A116911/b116911.txt">Table of n, a(n) for n = 1..1000</a>
%F A116911 A000040 INTERSECTION {Partial sums of A116995(n)}. (Sum_{i=1..k} A000326(A000040(i))) iff in A000040. (Sum_{i=1..k} prime(i)*(3*prime(i)-1)/2) iff in A000040.
%e A116911 a(1) = Sum_{i=1..1} prime(i)*(3*prime(i)-1)/2 = P(2) = 5.
%e A116911 a(2) = Sum_{i=1..2} prime(i)*(3*prime(i)-1)/2 = P(2) + P(3) = 17.
%e A116911 a(3) = Sum_{i=1..11} prime(i)*(3*prime(i)-1)/2 = P(2) + P(3) + P(5) + P(7) + P(11) + P(13) + P(17) + P(19) + P(23) + P(29) + P(31) = 4957.
%e A116911 a(4) = P(2) + ... + P(103) = 129277.
%p A116911 P:=n->n*(3*n-1)/2: seq(P(n),n=0..10): a:=proc(n) if isprime(sum(P(ithprime(j)),j=1..n))=true then sum(P(ithprime(j)),j=1..n) else fi end: seq(a(n),n=1..600); # _Emeric Deutsch_, Apr 15 2006
%t A116911 Module[{nn=4000,pn,pr},pn=PolygonalNumber[5,Range[nn]];pr=Table[If[ PrimeQ[ n],1,0],{n,nn}];Select[Accumulate[Pick[pn,pr,1]],PrimeQ]] (* _Harvey P. Dale_, Jan 27 2020 *)
%Y A116911 Cf. A000040, A000217, A034953, A085739, A116994, A116995.
%K A116911 easy,nonn
%O A116911 1,1
%A A116911 _Jonathan Vos Post_, Apr 03 2006
%E A116911 More terms from _Emeric Deutsch_, Apr 15 2006