A136510 Smallest k>1 such that in binary representation n is contained in n^k.

2, 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, 5

Offset: 1

Author

Reinhard Zumkeller, Jan 03 2008

Keywords

• nonn
• base

Comments

A136511(n) = n^a(n);

a(A018826(n)) = 2; 1 < a(A136490(n)) <= 3;

conjecture: a(n) is defined for all n.

Links

• R. Zumkeller, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to binary expansion of n

Crossrefs

Variant of A086063.

Programs

Mathematica

Table[Module[{k=2},While[SequenceCount[IntegerDigits[n^k,2],IntegerDigits[ n,2]]==0,k++];k],{n,110}] (* Harvey P. Dale, Aug 20 2020 *)