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 A117503 #19 Apr 21 2024 11:39:10
%S A117503 613,6229,7607,9679,46133,61469,69191,120067,211663,285049,316697,
%T A117503 354323,402371,444979,481109,490313,532709,993907,1055543,1083721,
%U A117503 1237487,1329701,1409977,1442899,1484671,1656199,1700471,1874767
%N A117503 Primes among partial sums of floor(Pi*prime(k)), k=1,2,3,....
%C A117503 Modeled on the same concept as cumulative sums of squared primes in A098562.
%F A117503 Define the sequence s as s(j) = Sum_{k=1..j} floor(Pi*prime(k)) for j >= 1; then a(n) is the n-th prime in the sequence s.
%p A117503 Digits := 30 ; A117503 := proc(nmax) local a,pisum,p ; a := [] ; pisum := 0 ; p :=1 ; while nops(a) <=nmax do while true do pisum := pisum+floor(Pi*ithprime(p)) ; p := p+1 ; if isprime(pisum) then a := [op(a),pisum] ; break ; fi ; od : od : RETURN(a) ; end: a := A117503(30) ; # _R. J. Mathar_, Oct 26 2006
%t A117503 Select[Accumulate[Floor[Pi Prime[Range[800]]]],PrimeQ] (* _Harvey P. Dale_, Jun 06 2022 *)
%o A117503 (UBASIC)
%o A117503 10 Ct=1
%o A117503 20 B=nxtprm(B)
%o A117503 30 C=int(pi(B))
%o A117503 40 D=D+C
%o A117503 41 print Ct,B,C,D
%o A117503 50 if D=prmdiv(D) then print D:stop
%o A117503 55 Ct=Ct+1
%o A117503 60 goto 20
%Y A117503 Cf. A117504, A098562.
%K A117503 easy,nonn,less
%O A117503 1,1
%A A117503 _Enoch Haga_, Mar 25 2006
%E A117503 Edited by _Jon E. Schoenfield_, Sep 23 2018