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
Examples
4 is in the sequence because 4^4+1 = 257 and 6^4+1 = 1297 are both prime.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Programs
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Magma
[n: n in [0..3300] | IsPrime(n^4 + 1) and IsPrime((n + 2)^4 + 1)]; // Vincenzo Librandi, Oct 13 2012
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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:
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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 *)