A197227 -id:A197227 - cp's OEIS frontend

A067377 Primes expressible as the sum of (at least two) consecutive primes in at least 1 way.

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, 647, 659, 661, 677, 683, 691, 701, 719

Offset: 1

Patrick De Geest, Feb 04 2002

nonn

			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

Hans Havermann, Table of n, a(n) for n = 1..34589
Patrick De Geest, WONplate 122
Hans Havermann, List of possible number of consecutive primes for n = 1..293768
Carlos Rivera, Puzzle 46. Primes expressible as sum of consecutive primes in K ways, The Prime Puzzles and Problems Connection.

Cf. A050936, A067372-A067381, A307610.

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

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 *)

Prime(n) such that A307610(n) > 1. - Ray Chandler, Sep 21 2023

Offset changed to 1 by Hans Havermann, Oct 07 2018

A037174 Primes which are not the sum of consecutive composite numbers.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 47, 61, 73, 107, 167, 179, 313, 347, 421, 479, 719, 863, 1153, 1213, 1283, 1307, 1523, 3467, 3733, 4007, 4621, 4787, 5087, 5113, 5413, 7523, 7703, 9817, 10333, 12347, 12539, 13381, 17027, 18553, 19717, 19813, 23399, 26003, 31873, 36097, 38833

Offset: 1

Naohiro Nomoto

nonn

It seems reasonable that a(n)/A079149(n) has an asymptote that could be estimated. - Peter Munn, Aug 21 2023

T. D. Noe, Table of n, a(n) for n = 1..3492 (terms less than 2*10^9)

Subsequence of A079149.
With {1}, the complement of A133576.
Primes that are the sum of specific numbers of consecutive composite numbers: A060254 (2), A060328 (3), A060329 (4), A060330 (5), A060331 (6), A060332 (7), A060333 (8).
Cf. A050940, A197227.

N:= 5000:
primes,comps:= selectremove(isprime,{$2..N}):
M:= nops(comps):
X:= primes:
for n from 1 to floor(sqrt(2*N)) do
i:= 1;
T:= add(comps[k],k=1..n);
while T <= N do
X := X minus {T};
if i + n > M then break fi;
T := T + comps[i+n] - comps[i];
i := i+1;
od;
od:
X;
# Robert Israel, Jun 24 2008

More terms from Jud McCranie, Jul 12 2000

Corrected by T. D. Noe, Aug 15 2008

cp's OEIS Frontend

A067377 Primes expressible as the sum of (at least two) consecutive primes in at least 1 way.

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