A262281 -id:A262281 - cp's OEIS frontend

A261922 a(n) = smallest nonnegative number that is not a substring of n in its binary representation.

1, 0, 3, 0, 3, 3, 4, 0, 3, 3, 3, 4, 5, 4, 4, 0, 3, 3, 3, 5, 3, 3, 4, 4, 5, 5, 4, 4, 5, 4, 4, 0, 3, 3, 3, 5, 3, 3, 5, 5, 3, 3, 3, 4, 7, 4, 4, 4, 5, 5, 5, 5, 7, 4, 4, 4, 5, 5, 4, 4, 5, 4, 4, 0, 3, 3, 3, 5, 3, 3, 5, 5, 3, 3, 3, 6, 5, 7, 5, 5, 3, 3, 3, 6, 3, 3, 4, 4, 7, 7, 4, 4, 8, 4, 4, 4, 5, 5, 5, 5, 5, 7

Offset: 0

N. J. A. Sloane, Sep 16 2015

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Similar to A261461.

Cf. A007088, A030308, A062289, A126646, A262281.

import Data.List (isInfixOf)
a261922 x = f a030308_tabf where
   f (cs:css) = if isInfixOf cs (a030308_row x)
                   then f css else foldr (\d v -> 2 * v + d) 0 cs
-- Reinhard Zumkeller, Sep 17 2015

bstr(n) = if (n==0, "0", my(s="", b=binary(n)); for (i=1, #b, s=concat(s, b[i])); s);
a(n) = my(sn=btostr(n), k=0); while (#strsplit(sn, bstr(k)) != 1, k++); k; \\ Michel Marcus, Sep 20 2023

def a(n): b=bin(n)[2:]; return next(k for k in range(2**len(b)) if bin(k)[2:] not in b)
print([a(n) for n in range(99)]) # Michael S. Branicky, Sep 21 2023

From Reinhard Zumkeller, Sep 17 2015: (Start)
a(A062289(n)) = A261461(A062289(n)).
a(A126646(n)) != A261461(A126646(n)). (End)

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

Original entry on oeis.org

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

N. J. A. Sloane, Sep 19 2015

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

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

Cf. A261416, A261461, A261922.

See A262281 for the "nonnegative" version.

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 *)

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

cp's OEIS Frontend

A261922 a(n) = smallest nonnegative number that is not a substring of n in its binary representation.

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