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%I #9 Aug 31 2017 11:26:20
%S 3,68491,1472837,20933977,115763405909,860612330076805920786264707,
%T 295312333859267885313149356219,
%U 3030645565448009172324576658633624992466799,1438089684181622246462815859549895702132195129054882453928357949021844283495791173
%N Primes of the form (2n-1)^(2n-1) mod 2^(2n-1).
%C Primes for n's: 2, 10, 11, 13, 19, 46, 50, 72, 139, 162, 344, 739, 1757, 3439, (10000)..., .
%t f[n_] := Block[{a = PowerMod[2 n - 1, 2 n - 1, 2^(2 n - 1)]}, If[ PrimeQ@ a, a, 0]]; k = 1; lst = {}; While[k < 100, a = f@ k; If[a != 0, AppendTo[lst, a]]; k++]; lst
%t pfQ[n_]:=Module[{c=2n-1},PowerMod[c,c,2^c]]; Select[Table[pfQ[n],{n,200}],PrimeQ] (* _Harvey P. Dale_, Aug 31 2017 *)
%Y Cf. A000040, A000079, A000312, A178537.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Jan 01 2011
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