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A339774 a(n) is the least k such that 3^k == A047471(n) (mod 2^A047471(n)).

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%I A339774 #9 Dec 16 2020 19:25:29
%S A339774 0,1,2,39,23988,2685,1079830,3,1798749736,7936950713,314244766442,
%T A339774 895397198495,65283613526364,203550894972341,27025091041430142,
%U A339774 54487836217255419,2756442714229679952,34856858877609547377,2262552012902592868562,4616799241038411627031,4,116433218705414728492013
%N A339774 a(n) is the least k such that 3^k == A047471(n) (mod 2^A047471(n)).
%C A339774 For n >= 3, 3^x == y (mod 2^n) has solutions x if and only if y is in A047471.
%H A339774 Robert Israel, <a href="/A339774/b339774.txt">Table of n, a(n) for n = 1..831</a>
%F A339774 a((3^k - (-1)^k)/4 + 1) = k.
%e A339774 a(4) = 39 because A047471(4) = 11 and 3^39 == 11 (mod 2^11).
%p A339774 f:= proc(n) local k,v;
%p A339774   v:= subs(msolve(3^k=n,2^n),k);
%p A339774   subs(op(indets(v))=0,v)
%p A339774 end proc:
%p A339774 seq(seq(f(8*i+j),j=[1,3]),i=0..10);
%Y A339774 Cf. A047471.
%K A339774 nonn
%O A339774 1,3
%A A339774 _J. M. Bergot_ and _Robert Israel_, Dec 16 2020