

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
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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 nPn 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



