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%I #38 Oct 04 2023 12:12:12
%S 2,17,2,2424833,2,769,2
%N Smallest prime factor of n^(n^n) + 1.
%C Other known values: a(10)=307201, a(12)=10871635969, a(14)=977502209. - _Arkadiusz Wesolowski_, Jan 29 2012
%C a(8) > 10^20. - _Max Alekseyev_, Jul 31 2015
%C 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
%C a(18) = 28311553. - _Chai Wah Wu_, May 18 2020
%C a(16) = 4457323664018586376077313, a(20) = 46179488366593. - _Max Alekseyev_, Aug 29 2023
%H G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/1.html">Prime Curios! 2424833</a>
%F a(2*n-1) = 2.
%t 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 *)
%K hard,more,nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Nov 04 2011
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