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A217795 Numbers n such that n^4+1 and (n+2)^4+1 are both prime. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A141142 A007596 A050588 * A105282 A018325 A099804

Adjacent sequences:  A217792 A217793 A217794 * A217796 A217797 A217798

KEYWORD

nonn,easy

AUTHOR

Michel Lagneau, Oct 12 2012

STATUS

approved

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Last modified September 23 04:54 EDT 2020. Contains 337295 sequences. (Running on oeis4.)