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A065867 Primes which are the sum of a prime number of consecutive primes. 3
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 (list; graph; refs; listen; history; text; internal format)
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.

Cf. A138591. - Vladimir Joseph Stephan Orlovsky, Mar 25 2009

Sequence in context: A163587 A038922 A019367 * A071199 A082283 A238195

Adjacent sequences:  A065864 A065865 A065866 * A065868 A065869 A065870

KEYWORD

nonn

AUTHOR

Henry Bottomley, Dec 07 2001

STATUS

approved

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Last modified April 23 02:15 EDT 2019. Contains 322380 sequences. (Running on oeis4.)