A199295 Smallest prime factor of n^(n^n) + 1.

2, 17, 2, 2424833, 2, 769, 2

Offset

1,1

Comments

Other known values: a(10)=307201, a(12)=10871635969, a(14)=977502209. - Arkadiusz Wesolowski, Jan 29 2012

a(8) > 10^20. - Max Alekseyev, Jul 31 2015

a(8) < 2^(2^24)+1 since 8^(8^8)+1 = (2^(2^24)+1) * (2^(2^25)-2^(2^24)+1) and 2^(2^24)+1 (the 24th Fermat number) is known to be composite. - Sean A. Irvine, Jun 27 2017

a(18) = 28311553. - Chai Wah Wu, May 18 2020

a(16) = 4457323664018586376077313, a(20) = 46179488366593. - Max Alekseyev, Aug 29 2023

Links

Table of n, a(n) for n=1..7.

G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 2424833

Formula

a(2*n-1) = 2.

Mathematica

lst = {}; r = 7; Do[k = 1; While[True, p = k*2^(n + 1) + 1; If[PrimeQ[p] && PowerMod[n, n^n, p] + 1 == p, Break[]]; k++]; AppendTo[lst, p], {n, 2, r, 2}]; lst = Flatten[Transpose@{Table[2, {Floor[r/2]}], lst}]; If[OddQ[r], AppendTo[lst, 2], lst] (* Arkadiusz Wesolowski, Jan 29 2012 *)

Crossrefs

Sequence in context: A275588 A114560 A108883 * A162623 A165234 A155895

Adjacent sequences: A199292 A199293 A199294 * A199296 A199297 A199298

Keyword

hard,more,nonn

Author

Arkadiusz Wesolowski, Nov 04 2011

Status

approved