A356060 a(n) is the least prime p such that 2*prime(n)^2 + p is the square of a prime.

17, 7, 71, 23, 47, 23, 263, 239, 311, 167, 887, 71, 359, 23, 71, 4583, 2447, 479, 431, 1367, 1223, 4679, 2351, 1319, 503, 2399, 983, 3671, 887, 1031, 503, 2927, 2063, 167, 7127, 4127, 431, 1151, 10271, 9311, 5087, 7919, 479, 4463, 8231, 887, 11447, 1031, 17351, 4679, 983, 7559, 5639, 2879, 2591

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

2*A001248(n) + a(n) = A356048(n)^2.

Example

a(3) = 71 because the third prime is 5, 2*5^2 + 71 = 121 = 11^2 where 11 is prime, and 71 is the least prime that works.

Maple

f:= proc(n) local q;
    q:= floor(sqrt(2)*n);
    do
      q:= nextprime(q);
      if isprime(q^2-2*n^2) then return q^2-2*n^2 fi;
    od
end proc:
map(f, [seq(ithprime(i), i=1..100)]);

Prog

(PARI) a(n) = my(p=2, q=prime(n), s); while (! (issquare(s=2*q^2+p) && isprime(sqrtint(s))), p = nextprime(p+1)); p; \\ Michel Marcus, Aug 04 2022

Crossrefs

Cf. A001248, A356048.

Sequence in context: A114032 A107807 A075710 * A048368 A040275 A355237

Adjacent sequences: A356057 A356058 A356059 * A356061 A356062 A356063

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jul 24 2022

Status

approved