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

1,1

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A027861.

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

Sequence in context: A237997 A317885 A321535 * A276846 A303665 A027947

Adjacent sequences: A108806 A108807 A108808 * A108810 A108811 A108812

Keyword

easy,nonn

Author

Walter Kehowski, Jul 04 2005

Status

approved