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

0,3

Links

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

Formula

From Reinhard Zumkeller, Sep 17 2015: (Start)

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

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

Prog

(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

Crossrefs

Similar to A261461.

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

Sequence in context: A270028 A167223 A341480 * A078907 A282135 A309339

Adjacent sequences: A261919 A261920 A261921 * A261923 A261924 A261925

Keyword

nonn,base

Author

N. J. A. Sloane, Sep 16 2015

Status

approved