%I #2 Mar 30 2012 18:40:51
%S 1,4,19,48,645,5346,9989,423680,4936673,22863284,717864203,
%T 10398234146,14778845999,2318706892436,41349958502663,67290481692176,
%U 1273710986008283,21639017114636720,1870679510063123381
%N Partial sums of A053519.
%C Partial sums of denominators of successive convergents to continued fraction 1+2/(3+3/(4+4/(5+5/(6+6/(7+7/(8+8/(9+9/10+...))))))). The subsequence of primes in this partial sum begins: 19, 1273710986008283.
%F a(n) = SUM[i=0..n] A053519(i).
%e a(16) = 1 + 3 + 15 + 29 + 597 + 4701 + 4643 + 413691 + 4512993 + 17926611 + 695000919 + 9680369943 + 4380611853 + 2303928046437 + 39031251610227 + 25940523189513 + 1206420504316107 = 1273710986008283 is prime.
%Y Cf. A053519, A053518, A053520, A053556, A053557.
%K easy,nonn
%O 0,2
%A _Jonathan Vos Post_, Mar 20 2010