A065867 Primes which are the sum of a prime number of consecutive primes.

5, 23, 31, 41, 53, 59, 67, 71, 83, 97, 101, 109, 131, 139, 173, 181, 197, 199, 211, 223, 233, 251, 263, 269, 271, 281, 311, 331, 349, 353, 373, 401, 421, 431, 439, 443, 449, 457, 463, 487, 491, 499, 503, 523, 563, 587, 593, 607, 617, 631, 647, 659, 661, 677

Offset

1,1

Links

Table of n, a(n) for n=1..54.

Example

5 = 2 + 3.
23 = 5 + 7 + 11.
31 = 7 + 11 + 13.
41 = 11 + 13 + 17.
53 = 5 + 7 + 11 + 13 + 17.

Mathematica

lst={}; Do[s=Prime[m]; k=1; Do[p=Prime[n]; s+=p; k++; If[PrimeQ[s]&&PrimeQ[k], If[s<=10837, AppendTo[lst, s]]], {n, m+1, 5*5!}], {m, 5*5!}]; lst=Take[Union@lst, 500] (* Vladimir Joseph Stephan Orlovsky, Sep 13 2009 *)
Module[{nn=60, prs}, prs=Prime[Range[nn]]; Take[Select[Union[ Flatten[ Table[ Total/@ Partition[prs, n, 1], {n, prs}]]], PrimeQ], nn]] (* Harvey P. Dale, Aug 12 2016 *)

Crossrefs

Cf. A001043, A034707, A034962, A034965, A138591.

Sequence in context: A163587 A038922 A019367 * A082283 A071199 A238195

Adjacent sequences: A065864 A065865 A065866 * A065868 A065869 A065870

Keyword

nonn

Author

Henry Bottomley, Dec 07 2001

Status

approved