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 A172034 #3 Mar 30 2012 18:40:50
%S A172034 23,52,111,172,239,310,389,472,581,718,857,1006,1199,1426,1659,1898,
%T A172034 2149,2406,2675,2946,3223,3516,3823,4134,4451,4810,5189,5572,5961,
%U A172034 6358,6759,7178,7609,8058,8519,8982,9449,9928,10427,10930,11451,12008,12571
%N A172034 Partial sums of Pillai primes (A063980).
%C A172034 The values alternate between odd and even. The first prime partial sum of Pillai primes is a(5) = 23 + 29 + 59 + 61 + 67 = 239. The second prime partial sum is a(7) = 389. The next such primes are a(11) = 857 (= the 72nd Pillai prime), a(23) = 3823, a(25) = 4451, a(27) = 5189. The coincidence which prompted this sequence is that the 266th Pillai prime is a(23), the sum of the first 23 Pillai primes. Curiously, 23 is the smallest Pillai prime. What are the next such Pillai primes in the partial sum?
%F A172034 a(n) = SUM[i=i..n]A063980(i) = SUM[i=i..n] {p: p prime and there exists an integer m such that m!+1 is 0 mod p and p is not 1 mod m}.
%e A172034 a(1) = 23 because 23 is the first Pillai prime A063980(1). a(2) = 52 because 23+29 = 52 is the sum of the first two Pillai primes A063980(1)+A063980(2).
%K A172034 nonn
%O A172034 1,1
%A A172034 _Jonathan Vos Post_, Jan 23 2010
%E A172034 More terms from _R. J. Mathar_, Jan 24 2010