A086063 a(n) = if n<=1 then 1 else smallest k>1 such that in binary representation n is contained in n^k.

1, 1, 2, 3, 2, 3, 3, 3, 2, 3, 3, 5, 3, 4, 3, 3, 2, 3, 3, 6, 3, 6, 5, 3, 3, 5, 5, 2, 3, 3, 3, 3, 2, 3, 3, 6, 3, 8, 6, 3, 3, 2, 9, 4, 5, 6, 5, 5, 3, 5, 5, 4, 5, 6, 2, 5, 3, 5, 3, 6, 3, 6, 3, 3, 2, 3, 3, 6, 3, 7, 6, 10, 3, 9, 11, 5, 7, 8, 4, 5, 3, 9, 2, 8, 9, 7, 4, 6, 5, 6, 6, 3, 5, 5, 5, 5, 3, 5, 5, 3, 5, 9, 11, 7

Offset

0,3

Comments

A094543(n) = n^a(n).

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Example

n=6: 6='110' is not contained in 6^2='100100', but in 6^3='11011000', therefore a(6)=3.

Mathematica

brn[n_]:=Module[{k=2, idn2=IntegerDigits[n, 2]}, While[SequenceCount[IntegerDigits[n^k, 2], idn2]<1, k++]; k]; Join[{1, 1}, Array[brn, 110, 2]] (* Harvey P. Dale, Nov 30 2025 *)

Crossrefs

Cf. A045537, A007088.

Sequence in context: A283617 A164886 A091935 * A145653 A346153 A266119

Adjacent sequences: A086060 A086061 A086062 * A086064 A086065 A086066

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 24 2003

Extensions

Extended and corrected by Reinhard Zumkeller, May 08 2004

Status

approved