A348790 -id:A348790 - cp's OEIS frontend

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

Henry Bottomley, Dec 07 2001

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001043, A034707, A034962, A034965, A138591, A348790, A348791.

Cf. A034962 (subsequence).

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 *)

A348791 a(n) is the smallest prime that can be written as the sum of a prime number of consecutive primes in exactly n ways, or -1 if no such number exists.

Original entry on oeis.org

1, 5, 83, 863, 311, 1837067, 254298349, 2372135461

Offset: 0

Harvey P. Dale and N. J. A. Sloane, Nov 30 2021

			a(2) = 83 from 83 = 11+13+17+19+23 (5 primes) = 23+29+31 (3 primes).
a(4) = 311 from
  311 = 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 (11 primes)
  = 31 + 37 + 41 + 43 + 47 + 53 + 59 (7 primes)
  = 53 + 59 + 61 + 67 + 71 (5 primes)
  = 101 + 103 + 107 (3 primes).

Cf. A082283.

See A348790 for a different version.

a(6) from Michael S. Branicky, Nov 30 2021

a(7) from Michael S. Branicky, Dec 01 2021

cp's OEIS Frontend

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

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