A256246 Numbers n such that 2*n + prime(n) is a square.

1, 6, 10, 75, 140, 302, 463, 951, 989, 1219, 1297, 1681, 1776, 1877, 1921, 2379, 2662, 2769, 2828, 3499, 3763, 4810, 4959, 5424, 6156, 6238, 6319, 6829, 7820, 8013, 8108, 9178, 11831, 13570, 13939, 14309, 14677, 17661, 19456, 19894, 21946, 22084, 23148, 23470

Offset

1,2

Links

Zak Seidov, Table of n, a(n) for n = 1..252

Example

a(1) = 1 because 2*n + prime(n) = 2*1 + 2 = 4 = 2^2,
a(2) = 6 because 2*n + prime(n) = 2*6 + 13 = 25 = 5^2,
a(3) = 10 because 2*n + prime(n) = 2*10 + 29 = 49 = 7^2.

Mathematica

Transpose[Select[Table[{2 n, Prime[n]}, {n, 25000}], IntegerQ[Sqrt[Total[#]]]&]][[1]]/2 (* Vincenzo Librandi, Mar 21 2015 *)
Select[Range[25000], IntegerQ[Sqrt[2*#+Prime[#]]]&] (* Harvey P. Dale, Jun 17 2018 *)

Prog

(Magma) [n: n in [1..3*10^4] | IsSquare(2*n + NthPrime(n))]; // Vincenzo Librandi, Mar 21 2015
(PARI) for(n=1, 10^4, if(issquare(2*n+prime(n)), print1(n, ", "))) \\ Derek Orr, Mar 22 2015

Crossrefs

Cf. A064371, A256247.

Sequence in context: A105157 A166386 A280881 * A246800 A269341 A348650

Adjacent sequences: A256243 A256244 A256245 * A256247 A256248 A256249

Keyword

nonn

Author

Zak Seidov, Mar 20 2015

Status

approved