A309770 Numbers that are sums of one or more consecutive primes in more than one way.

5, 17, 23, 31, 36, 41, 53, 59, 60, 67, 71, 72, 83, 90, 97, 100, 101, 109, 112, 119, 120, 127, 131, 138, 139, 143, 152, 173, 180, 181, 187, 197, 199, 204, 210, 211, 221, 223, 228, 233, 240, 251, 258, 263, 269, 271, 276, 281, 287, 300, 304, 311, 323, 330, 331, 340, 349

Offset

1,1

Comments

Contains A067372 as a subsequence.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Prime Sums

Formula

A054845(a(n)) > 1.

Example

5 is in the sequence because it can be written as either 5 or 2 + 3.
36 is the sequence because it can be written as either 5 + 7 + 11 + 13 or 17 + 19.

Maple

N:= 1000: # for terms <= N
P:= select(isprime, [2, seq(i, i=3..N, 2)]):
S:= [0, op(ListTools:-PartialSums(P))]:
V:= Vector(N):
for i from 1 to nops(S) do
  for j from i-1 to 1 by -1 do
    v:= S[i]-S[j];
    if v > N then break fi;
    V[v]:= V[v]+1;
od od:
select(t -> V[t]>1, [$1..N]); # Robert Israel, Aug 22 2019

Crossrefs

Cf. A000040, A034707, A050936, A054845, A054996, A067372, A067377.

Sequence in context: A307471 A226671 A226674 * A054997 A067377 A337095

Adjacent sequences: A309767 A309768 A309769 * A309771 A309772 A309773

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 16 2019

Status

approved