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A067377 Primes expressible as the sum of (at least two) consecutive primes in at least 1 way. 6
5, 17, 23, 31, 41, 53, 59, 67, 71, 83, 97, 101, 109, 127, 131, 139, 173, 181, 197, 199, 211, 223, 233, 251, 263, 269, 271, 281, 311, 331, 349, 353, 373, 379, 401, 421, 431, 439, 443, 449, 457, 463, 479, 487, 491, 499, 503, 523, 563, 587, 593, 607, 617, 631 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Hans Havermann, Table of n, a(n) for n = 1..34589

P. De Geest, WONplate 122

Hans Havermann Table of n, a(n), list of possible number of consecutives for n = 1..293768

C. Rivera, Puzzle 46

EXAMPLE

The prime 83, for example, is the sum of the five consecutive primes 11 + 13 + 17 + 19 + 23.

The prime 2011, for example, is the sum of the eleven consecutive primes 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211. - Daniel Forgues, Nov 03 2011

MATHEMATICA

p = {}; Do[a = Table[ Prime[i], {i, n, 150}]; l = Length[a]; k = 2; While[k < l + 1, b = Plus @@@ Partition[a, k]; k++; p = Append[ p, Select[ b, PrimeQ[ # ] &]]], {n, 1, 149}]; Take[ Union[ Flatten[p]], 70]

m=5!; lst={}; Do[p=Prime[a]; Do[p+=Prime[b]; If[PrimeQ[p]&&p<=Prime[m]*3+8, AppendTo[lst, p]], {b, a+1, m+2, 1}], {a, m}]; Union[lst] (* Vladimir Joseph Stephan Orlovsky, Aug 15 2009 *)

CROSSREFS

Cf. A050936, A067372-A067381.

Cf. A197227 (primes that are not the sum of consecutive primes).

Sequence in context: A226671 A226674 A054997 * A153504 A044438 A101414

Adjacent sequences:  A067374 A067375 A067376 * A067378 A067379 A067380

KEYWORD

nonn

AUTHOR

Patrick De Geest, Feb 04 2002

EXTENSIONS

Offset changed to 1 by Hans Havermann, Oct 07 2018

STATUS

approved

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Last modified October 22 23:18 EDT 2018. Contains 316518 sequences. (Running on oeis4.)