A216945 Numbers k such that k-2, k^2-2, k^3-2, k^4-2 and k^5-2 are all prime.

15331, 289311, 487899, 798385, 1685775, 1790991, 1885261, 1920619, 1967925, 2304805, 2479735, 3049201, 3114439, 3175039, 3692065, 4095531, 4653649, 5606349, 5708235, 6113745, 6143235, 6697425, 7028035, 7461601, 8671585, 8997121, 9260131, 10084915, 10239529

Offset

1,1

Comments

k^6-2 is also prime for k = 1685775, 4095531, 4653649, 5606349, 13219339, 13326069, 18439561, ...

Sequence is infinite under Schinzel's Hypothesis H. a(n) >> n log^5 n. - Charles R Greathouse IV, Sep 20 2012

Links

Table of n, a(n) for n=1..29.

Formula

Sequence is A052147 intersection A028870 intersection A038599 intersection A154831 intersection A154833.

Mathematica

Select[Range[20000000], And@@PrimeQ/@(Table[n^i-2, {i, 1, 5}]/.n->#)&]
Select[Prime[Range[680000]]+2, AllTrue[#^Range[2, 5]-2, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 11 2020 *)

Crossrefs

Cf. A052147, A028870, A038599, A154831, A154833, A154935.

Sequence in context: A233594 A064982 A204317 * A258572 A352477 A232382

Adjacent sequences: A216942 A216943 A216944 * A216946 A216947 A216948

Keyword

nonn

Author

Michel Lagneau, Sep 20 2012

Status

approved