A161959 Smallest composite number which is the sum of n consecutive prime numbers.

8, 10, 26, 28, 56, 58, 77, 100, 129, 160, 236, 238, 326, 328, 381, 440, 501, 568, 639, 712, 791, 874, 963, 1060, 1161, 1264, 1371, 1480, 1593, 1720, 1851, 1988, 2127, 2276, 2427, 2584, 2747, 2914, 3087, 3266, 3447, 3638, 3831, 4028, 4227, 4438, 4661, 4888

Offset

2,1

Links

Table of n, a(n) for n=2..49.

Formula

a(2n+1) = A007504(2n+1)

a(2n) = A007504(2n) if that value is composite, else A007504(2n+1) - 2.

a(n) ~ n^2 * log(n) / 2.

Example

a(6) = 56 = 3 + 5 + 7 + 11 + 13 + 17. (2 + 3 + 5 + 7 + 11 + 13 is prime so not a member of this sequence.)

Mathematica

With[{prs=Prime[Range[500]]}, Table[SelectFirst[Total/@Partition[ prs, n, 1], CompositeQ], {n, 2, 50}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 15 2019 *)

Crossrefs

Sequence in context: A182366 A347194 A271313 * A236751 A259713 A096516

Adjacent sequences: A161956 A161957 A161958 * A161960 A161961 A161962

Keyword

nonn

Author

Claudio Meller, Jun 22 2009

Status

approved