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 A140126 #8 Jan 29 2017 11:00:28
%S A140126 1,3,6,11,18,26,36,48,61,79,99,126,154,187,224,266,311,358,413,471,
%T A140126 531,593,656,721,788,861,936,1014,1094,1179,1267,1357,1449,1551,1654,
%U A140126 1759,1871,1986,2104,2224,2349,2477,2607,2739,2874,3014,3156,3306,3459,3616
%N A140126 Partial sums of A001912.
%F A140126 a(n) = SUM[i=1..n] A001912(i) = SUM[j=1..n] {Numbers i_j such that 4*(i_j)^2 + 1 is prime}.
%e A140126 a(17) = 1 + 2 + 3 + 5 + 7 + 8 + 10 + 12 + 13 + 18 + 20 + 27 + 28 + 33 + 37 + 42 + 45 = 311 which is itself a prime. The primes in this sequence begin: 3, 11, 61, 79, 311, 593.
%p A140126 A001912 := proc(n) option remember ; local a ; if n <= 3 then RETURN(n); else for a from A001912(n-1)+1 do if isprime(4*a^2+1) then RETURN(a) ; fi ; od: fi ; end: A140126 := proc(n) local i ; add( A001912(i),i=1..n) ; end: seq(A140126(n),n=1..80) ; # _R. J. Mathar_, Jun 12 2008
%t A140126 Accumulate[Select[Range[200],PrimeQ[4#^2+1]&]] (* _Harvey P. Dale_, Jan 29 2017 *)
%Y A140126 Cf. A000040, A001912, A002496, A005574, A062325, A090693.
%K A140126 easy,nonn
%O A140126 1,2
%A A140126 _Jonathan Vos Post_, Jun 04 2008
%E A140126 More terms from _R. J. Mathar_, Jun 12 2008