A086063 -id:A086063 - cp's OEIS frontend

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

Reinhard Zumkeller, Jan 03 2008

A136511(n) = n^a(n);
a(A018826(n)) = 2; 1 < a(A136490(n)) <= 3;
conjecture: a(n) is defined for all n.

Variant of A086063.

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

A094543 Smallest perfect power of n containing n in binary representation.

Original entry on oeis.org

0, 1, 4, 27, 16, 125, 216, 343, 64, 729, 1000, 161051, 1728, 28561, 2744, 3375, 256, 4913, 5832, 47045881, 8000, 85766121, 5153632, 12167, 13824, 9765625, 11881376, 729, 21952, 24389, 27000, 29791, 1024, 35937, 39304, 1838265625

Offset: 0

Reinhard Zumkeller, May 08 2004

nonn

a(n) = n^A086063(n).

			n=30='11110' is not contained in 30^2 = 900 = '1110000100' but in
a(3) = 30^3 = 27000 = '110100101111000'.

Cf. A007088.

cp's OEIS Frontend

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

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