A338985 a(n) is the first prime p such that the sum of 2*n consecutive primes starting at p is an oblong number, or 0 if there is no such p.

5, 13, 3, 13, 37, 137, 139, 283, 7, 37, 31, 73, 41, 457, 67, 757, 2351, 2591, 43, 1637, 19, 2437, 157, 5, 881, 4801, 59, 229, 4349, 2333, 11, 31, 1759, 1277, 53, 653, 3109, 307, 373, 4877, 241, 3719, 3301, 467, 3517, 197, 1297, 193, 1033, 941, 2141, 12041, 601, 599, 1753, 6317, 4969, 43, 5153

Offset

1,1

Comments

Conjecture: all a(n) > 0.

Links

Robert Israel, Table of n, a(n) for n = 1..2845

Example

a(4) = 13 because the sum of the four consecutive primes starting at 13 is 13+17+19+23=72 which is the oblong number 8*9, and this is the first prime for which the sum is an oblong number.

Maple

N:= 10^5: P:= select(isprime, [2, seq(i, i=3..N, 2)]):
S:= ListTools:-PartialSums([0, op(P)]):
nP:= nops(S):
f:= proc(n) local i;
  for i from 1 to nP-n do
    if issqr(1+4*(S[i+n]-S[i])) then return P[i] fi
  od;
  FAIL
end proc:
R:= NULL:
for i from 1 do
v:= f(2*i);
if v = FAIL then break fi;
R:= R, v
od:
R;

Crossrefs

Cf. A002378.

Sequence in context: A065934 A282063 A035412 * A065865 A088618 A121645

Adjacent sequences: A338982 A338983 A338984 * A338986 A338987 A338988

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 20 2020

Status

approved