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A338990 a(n) is the first prime p such that the sum of 2*n consecutive primes starting at p is (q-1)*q where q is prime, or 0 if there is no such p. 2
19, 61, 17, 8581, 10883, 151, 2083, 21859, 11813, 443, 6779, 1531, 21559, 37781, 7529, 757, 29027, 2591, 12739, 1637, 491, 4759, 56269, 341179, 37441, 81547, 59, 229, 1814023, 363523, 12109, 21493, 247993, 248089, 3617, 357551, 3109, 138563, 66973, 100103, 6907, 44819, 136519, 2953, 13063, 31687 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..306

EXAMPLE

a(3) = 17 because the sum of the 2*3=6 consecutive primes starting at 17 is 17+19+23+29+31+37 = 156 = 12*13 where 13 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, A338989.

Sequence in context: A270818 A206426 A211145 * A158521 A141897 A031384

Adjacent sequences:  A338987 A338988 A338989 * A338991 A338992 A338993

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified January 28 03:20 EST 2022. Contains 350654 sequences. (Running on oeis4.)