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

Author

N. J. A. Sloane, Sep 16 2015

Keywords

• nonn
• base

Links

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

Crossrefs

Similar to A261461.

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

Programs

Haskell

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

PARI

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

Python

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

Formula

From Reinhard Zumkeller, Sep 17 2015: (Start)

a(A062289(n)) = A261461(A062289(n)).

a(A126646(n)) != A261461(A126646(n)). (End)