A219117 Numbers n such that n^1+n+1, n^2+n+1, n^3+n+1 and n^4+n+1 are all prime.

1, 2, 5, 6, 69, 131, 426, 1665, 2129, 2696, 5250, 7929, 9689, 13545, 14154, 14286, 16434, 19760, 25739, 27809, 29631, 36821, 41819, 46619, 48321, 59030, 60500, 61955, 62321, 73610, 77685, 79646, 80535, 82655, 85251, 86996, 91014, 96566, 97739, 105939, 108240

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Maple

select(t -> andmap(isprime, [2*t+1, t^2+t+1, t^3+t+1, t^4+t+1]), [$1..2*10^5]); # Robert Israel, Dec 15 2017

Prog

(Haskell)
a219117_list = filter (all (== 1) . p) [1..] where
   p x = map (a010051 . (+ (x + 1)) . (x ^)) [1..4]

Crossrefs

Cf. A057683 (subsequence); A010051.

Sequence in context: A055877 A288799 A281378 * A111190 A244434 A176007

Adjacent sequences: A219114 A219115 A219116 * A219118 A219119 A219120

Keyword

nonn

Author

Reinhard Zumkeller, Nov 12 2012

Status

approved