A323361 Least number of consecutive primes beginning with 2, the sum of which (A007504) exceeds e^n.

1, 2, 3, 5, 7, 11, 17, 26, 40, 62, 96, 151, 238, 376, 596, 947, 1508, 2407, 3849, 6167, 9895, 15899, 25578, 41198, 66429, 107215, 173198, 280014, 453053, 733544, 1188472, 1926703, 3125268, 5072127, 8235857, 13379208, 21744190, 35353755

Offset

0,2

Comments

The final primes in the sums are 2, 3, 5, 11, 17, 31, 59, 101, 173, 293, 503, 877, 1493, 2579, 4363, 7481, ..., .

Links

Table of n, a(n) for n=0..37.

Example

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

Mathematica

p = 2; k = s = 0; lst = {}; Do[ While[s < Exp[n], s = s + p; p = NextPrime@ p; k++]; AppendTo[lst, k], {n, 60}]; lst

Crossrefs

Cf. A007504, A323360, A323362.

Sequence in context: A002379 A072465 A204631 * A052284 A133670 A356627

Adjacent sequences: A323358 A323359 A323360 * A323362 A323363 A323364

Keyword

nonn

Author

Robert G. Wilson v, Jan 12 2019

Status

approved