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

1,3

Comments

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

Links

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

Formula

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

Example

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

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);

Crossrefs

Cf. A047471.

Sequence in context: A274574 A212615 A247878 * A232086 A356683 A047660

Adjacent sequences: A339771 A339772 A339773 * A339775 A339776 A339777

Keyword

nonn

Author

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

Status

approved