A217795 Numbers n such that n^4+1 and (n+2)^4+1 are both prime.

2, 4, 46, 54, 80, 88, 140, 276, 492, 554, 566, 582, 730, 758, 786, 798, 912, 928, 1142, 1150, 1200, 1236, 1404, 1540, 1552, 1610, 1644, 1650, 1932, 1942, 2044, 2102, 2204, 2222, 2224, 2238, 2254, 2374, 2436, 2486, 2510, 2640, 2674, 2698, 2732, 2734, 3244, 3286

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

4 is in the sequence because 4^4+1 = 257 and 6^4+1 = 1297 are both prime.

Maple

for n from 0 by 2 to 3500 do: if type(n^4+1, prime)=true and type((n+2)^4+1, prime)=true then printf(`%d, `, n):else fi:od:

Mathematica

lst={}; Do[p=n^4+1; q=(n+2)^4+1; If[PrimeQ[p] && PrimeQ[q], AppendTo[lst, n]], {n, 0, 3000}]; lst
Select[Range[3500], AllTrue[{#^4+1, (#+2)^4+1}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 29 2015 *)

Prog

(Magma) [n: n in [0..3300] | IsPrime(n^4 + 1) and IsPrime((n + 2)^4 + 1)]; // Vincenzo Librandi, Oct 13 2012

Crossrefs

Cf. A000068, A002523, A037896.

Sequence in context: A353797 A007596 A050588 * A105282 A348247 A018325

Adjacent sequences: A217792 A217793 A217794 * A217796 A217797 A217798

Keyword

nonn,easy

Author

Michel Lagneau, Oct 12 2012

Status

approved