A231152 - OEIS

%I #8 Dec 04 2016 19:46:33

%S 2,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,8,8,8,9,9,9,10,10,10,11,11,11,12,

%T 12,13,13,13,14,14,14,15,15,16,16,16,17,17,17,18,18,19,19,19,20,20,20,

%U 21,21,21,22,22,23,23,23,24,24,24,25,25,25,26,26,27

%N Least integer k such that prime(n+1) + ... + prime(n+k) > prime(1) + ... + prime(n).

%C a(n) is the greatest k such that 2*s(n) >= s(n+k), where s(n) is the n-th partial sum of primes.

%F a(n) = A231153(n) + 1.

%e 5 <= 2 + 3 < 5 + 7, so a(2) = 2.

%e 19 + 23 <= 2 + 3 + 5 + 7 + 11 + 13 + 17 < 19 + 23 + 27, so a(7) = 3.

%t test = 0; u = Table[test = test + Prime[n]; tmp = 0; NestWhile[# + 1 &, n, test >= (tmp = tmp + Prime[#]) &] - n, {n, 1, 80}]; u + 1  (* _Peter J. C. Moses_, Nov 02 2013 *)

%Y Cf. A231151, A231153.

%K nonn,easy

%O 2,1

%A _Clark Kimberling_, Nov 09 2013