A262289 a(n) = smallest positive number, not a power of 2, that is not a substring of n in its binary representation.

3, 3, 3, 5, 3, 3, 5, 5, 3, 3, 3, 6, 5, 7, 5, 5, 3, 3, 3, 5, 3, 3, 7, 6, 5, 5, 7, 7, 5, 9, 5, 5, 3, 3, 3, 5, 3, 3, 5, 5, 3, 3, 3, 6, 7, 7, 9, 6, 5, 5, 5, 5, 7, 7, 7, 9, 5, 5, 9, 9, 5, 9, 5, 5, 3, 3, 3, 5, 3, 3, 5, 5, 3, 3, 3, 6, 5, 7, 5, 5, 3, 3, 3, 6, 3, 3, 7

Offset: 0

Author

N. J. A. Sloane, Sep 19 2015

Keywords

• nonn
• base

Comments

Similar to A261461, but if the smallest missing number is a power of 2, ignore it and look at the next-smallest missing number.

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 0..10000
• David Consiglio, Jr., Python Program

Crossrefs

Cf. A261416, A261461, A261922.

See A262281 for the "nonnegative" version.

Programs

Mathematica

fQ[m_, n_] := Block[{g}, g[x_] := ToString@FromDigits@IntegerDigits[x, 2]; StringContainsQ[g@ n, g@ m]]; Table[k = 3; While[Or[fQ[k, n] && k < 2 n, IntegerQ@ Log[2, k]], k++]; k, {n, 0, 86}] (* Michael De Vlieger, Sep 21 2015 *)

Extensions

a(23)-a(86) from Hiroaki Yamanouchi, Sep 20 2015