A338989 a(n) is the first prime p such that the sum of 2*n consecutive primes starting at p is q*(q+1) where q is prime, or 0 if there is no such p.

5, 71, 3, 977, 37, 7829, 8681, 283, 14341, 37181, 31, 8839, 1181, 60901, 54727, 2579, 64901, 1248019, 43, 141803, 47, 29881, 991, 5, 881, 1603919, 31123, 18679, 174149, 74149, 11, 1328269, 925513, 447859, 61, 890969, 5867, 35759, 4093, 27239, 1549, 6551, 1901987, 4597, 64781, 307, 13121, 353

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..141

Example

a(3) = 3 because the sum of the 2*3=6 consecutive primes starting at 3 is 3+5+7+11+13+17 = 56 = 7*(7+1) where 7 is prime.
a(4) = 977 because the sum of the 2*4=8 consecutive primes starting at 977 is 977+983+991+997+1009+1013+1019+1021 = 8010 = 89*(89+1) where 89 is prime.

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])) and isprime((sqrt(1+4*(S[i+n]-S[i]))-1)/2)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. A338985, A338990.

Sequence in context: A015502 A303291 A324229 * A101019 A056266 A248367

Adjacent sequences: A338986 A338987 A338988 * A338990 A338991 A338992

Keyword

nonn

Author

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

Status

approved