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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 9 09:37 EST 2021. Contains 349627 sequences. (Running on oeis4.)