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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 21 10:25 EST 2022. Contains 350477 sequences. (Running on oeis4.)