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%I #14 Feb 16 2019 07:05:26
%S 1,2,3,5,7,11,17,26,40,62,96,151,238,376,596,947,1508,2407,3849,6167,
%T 9895,15899,25578,41198,66429,107215,173198,280014,453053,733544,
%U 1188472,1926703,3125268,5072127,8235857,13379208,21744190,35353755
%N Least number of consecutive primes beginning with 2, the sum of which (A007504) exceeds e^n.
%C The final primes in the sums are 2, 3, 5, 11, 17, 31, 59, 101, 173, 293, 503, 877, 1493, 2579, 4363, 7481, ..., .
%e For n=3, e^3 = 20.0855.... Since 2 + 3 + 5 + 7 = 17 < 20.0855... and 2 + 3 + 5 + 7 + 11 = 28 > 20.0855..., 5 primes are required, so a(3) = 5. - _Michael B. Porter_, Jan 19 2019
%t p = 2; k = s = 0; lst = {}; Do[ While[s < Exp[n], s = s + p; p = NextPrime@ p; k++]; AppendTo[lst, k], {n, 60}]; lst
%Y Cf. A007504, A323360, A323362.
%K nonn
%O 0,2
%A _Robert G. Wilson v_, Jan 12 2019
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