%I #2 Mar 30 2012 18:40:50

%S 3,8,15,26,39,56,75,98,129,172,233,312,413,540,707,898,1097,1410,1757,

%T 2458,4167,6784,10323,16130,26631,37322,48601,60992,75471,118208,

%U 201547,296916,414155,541186,680123,821202,1088219,1358206,1732527,2718718

%N Partial sums of Wagstaff numbers A000978.

%C The prime partial sums of Wagstaff numbers begin 3, 233, 1097, 201547, 680123. None of these but 3 is itself a Wagstaff number.

%F a(n) = SUM[i=1..n] {integers i such that (2^i + 1)/3 is prime}.

%e a(40) = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 31 + 43 + 61 + 79 + 101 + 127 + 167 + 191 + 199 + 313 + 347 + 701 + 1709 + 2617 + 3539 + 5807 + 10501 + 10691 + 11279 + 12391 + 14479 + 42737 + 83339 + 95369 + 117239 + 127031 + 138937 + 141079 + 267017 + 269987 + 374321 + 986191.

%Y Cf. A000040, A000978.

%K hard,nonn

%O 1,1

%A _Jonathan Vos Post_, Jan 30 2010