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

0, 1, 2, 39, 23988, 2685, 1079830, 3, 1798749736, 7936950713, 314244766442, 895397198495, 65283613526364, 203550894972341, 27025091041430142, 54487836217255419, 2756442714229679952, 34856858877609547377, 2262552012902592868562, 4616799241038411627031, 4, 116433218705414728492013

Offset: 1

Author

J. M. Bergot and Robert Israel, Dec 16 2020

Keywords

• nonn

Comments

For n >= 3, 3^x == y (mod 2^n) has solutions x if and only if y is in A047471.

Examples

			a(4) = 39 because A047471(4) = 11 and 3^39 == 11 (mod 2^11).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..831

Crossrefs

Cf. A047471.

Programs

Maple

f:= proc(n) local k,v;
  v:= subs(msolve(3^k=n,2^n),k);
  subs(op(indets(v))=0,v)
end proc:
seq(seq(f(8*i+j),j=[1,3]),i=0..10);

Formula

a((3^k - (-1)^k)/4 + 1) = k.