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A178537 a(n) = (2n+1)^(2n+1) mod 2^(2n+1).

%I A178537 #22 Jun 27 2024 22:18:16
%S A178537 1,3,21,119,329,339,1533,2031,67857,68491,1472837,7105255,20933977,
%T A178537 91061443,344607757,137379807,942687265,22093239035,115763405909,
%U A178537 23058549975,581930881897,8126485230643,18131637168157,69459897210831,12202023051569,1785877136688747,4676672234192229,4337085752026823,51543753266508665,431102794881380259,338696479165696557
%N A178537 a(n) = (2n+1)^(2n+1) mod 2^(2n+1).
%H A178537 Robert G. Wilson v, <a href="/A178537/b178537.txt">Table of n, a(n) for n = 0..1000</a>
%F A178537 a(n) = A000312(2n+1) mod A000079(2n+1).
%p A178537 A178537 := proc(n)
%p A178537     local o ;
%p A178537     o := 2*n+1 ;
%p A178537     modp(o &^ o,2^o) ;
%p A178537 end proc: #  _R. J. Mathar_, Oct 10 2014
%t A178537 f[n_] := PowerMod[2n +1, 2n +1, 2^(2n +1)]; Array[f, 25, 0] (* _Robert G. Wilson v_, Dec 13 2016*)
%o A178537 (PARI) a(n)=lift(Mod(2*n+1,2^(2*n+1))^(2*n+1)) \\ _Charles R Greathouse IV_, Dec 13 2016
%Y A178537 Cf. A000079, A000312.
%K A178537 nonn
%O A178537 0,2
%A A178537 _Juri-Stepan Gerasimov_, Dec 24 2010