A108809 Numbers n such that both n+(n-1)^2 and n+(n+1)^2 are primes.

2, 3, 4, 7, 9, 15, 18, 25, 34, 55, 58, 63, 67, 100, 102, 139, 144, 148, 154, 162, 163, 168, 190, 195, 219, 232, 247, 267, 280, 289, 330, 349, 379, 384, 417, 427, 448, 454, 477, 568, 580, 643, 645, 669, 672, 727, 762, 793, 802, 813, 837, 847, 900, 975, 988, 993

Offset: 1

Author

Walter Kehowski, Jul 04 2005

Keywords

• easy
• nonn

Examples

			34 is in the sequence because 34 + 33^2 = 1123 and 34 + 35^2 = 1259 are both prime.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A027861.

Intersection of A055494 and A094210. - Michel Marcus, Feb 08 2017

Programs

Maple

L:=[]; for k from 1 to 1000 do if isprime(k+(k-1)^2) and isprime(k+(k+1)^2) then L:=[op(L),k] fi od;

Mathematica

Select[Range@1000, PrimeQ[#^2 - # + 1] && PrimeQ[#^2 + 3 # + 1] &] (* Ivan Neretin, Feb 08 2017 *)

PARI

isok(n) = isprime(n+(n-1)^2) && isprime(n+(n+1)^2); \\ Michel Marcus, Feb 08 2017