A067372 -id:A067372 - cp's OEIS frontend

A067376 Smallest integer expressible as the sum of (at least two) consecutive primes in n ways.

5, 36, 240, 311, 16277, 130638, 218918, 9186778, 274452156, 4611108324, 12941709050

Offset: 1

Patrick De Geest, Feb 04 2002

a(10)-a(11) found by Wilfred Whiteside in 2007 (see Rivera link). - Michael S. Branicky, Jul 27 2022

			In n=7 ways: 218918 = (#12,18199) (#16,13619) (#22,9851) (#28,7691) (#38,5623) (#46,4561) (#62,3301).

Patrick De Geest, WONplate 122
Carlos Rivera, Puzzle 46. Primes expressible as sum of consecutive primes in K ways, The Prime Puzzles and Problems Connection.

Cf. A050936, A067372-A067381, A054859.

Offset corrected and a(8)-a(9) from Donovan Johnson, Mar 14 2010

a(10) confirmed and a(10)-a(11) entered by Michael S. Branicky, Jul 27 2022

A163246 Squares which can be represented as the sum of consecutive primes in more than one way.

Original entry on oeis.org

36, 100, 576, 841, 961, 1764, 1849, 2209, 2304, 7056, 22801, 24649, 25600, 30276, 31684, 32400, 36481, 39601, 40000, 47524, 48400, 48841, 57600, 58081, 66564, 69169, 69696, 76729, 77284, 80089, 85849, 93636, 94864, 96721, 112896, 119716, 128164, 134689, 138384, 140625, 142884, 147456

Offset: 1

Gaurav Kumar, Jul 23 2009

nonn

			6^2 = 36 = 5 + 7 + 11 + 13 = 17 + 19.

Alois P. Heinz, Table of n, a(n) for n = 1..300

Cf. A000290, A034707, A050936, A067372, A084143, A163244.

{ A000290 } intersect { A034707 }.
{ A000290 } intersect { A050936 }.
k^2 such that A084143(k^2) > 1. - Georg Fischer, Jul 08 2022

Offset corrected by Arkadiusz Wesolowski, Mar 28 2012

Duplicate 2304 removed and some missing terms inserted by Georg Fischer, Jul 08 2022

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

Original entry on oeis.org

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

Ilya Gutkovskiy, Aug 16 2019

nonn

Contains A067372 as a subsequence.

			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.

Robert Israel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Prime Sums

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

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

A054845(a(n)) > 1.

cp's OEIS Frontend

A067376 Smallest integer expressible as the sum of (at least two) consecutive primes in n ways.

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A163246 Squares which can be represented as the sum of consecutive primes in more than one way.

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

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