A261461 - OEIS

A261461

a(n) is the smallest nonzero number that is not a substring of n in its binary representation.

1, 2, 3, 2, 3, 3, 4, 2, 3, 3, 3, 4, 5, 4, 4, 2, 3, 3, 3, 5, 3, 3, 4, 4, 5, 5, 4, 4, 5, 4, 4, 2, 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, 2, 3, 3, 3, 5, 3, 3, 5, 5, 3, 3, 3, 6, 5, 7, 5, 5, 3, 3, 3, 6, 3, 3

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

A261018(n) = a(A260273(n)).

Is a(n) = A091460(n) for n>1? - R. J. Mathar, Sep 02 2015. The lowest counterexample occurs at a(121) = 5 < 6 = A091460(121). - Álvar Ibeas, Sep 08 2020

a(A062289(n))=A261922(A062289(n)); a(A126646(n))!=A261922(A126646(n)). - Reinhard Zumkeller, Sep 17 2015

LINKS

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

David Consiglio, Jr., Python Program

FORMULA

a(n) = A144016(n) + 1 for any n > 0. - Rémy Sigrist, Mar 10 2018

MATHEMATICA

fQ[m_, n_] := Block[{g}, g[x_] := ToString@ FromDigits@ IntegerDigits[x, 2]; StringContainsQ[g@ n, g@ m]]; Table[k = 1; While[fQ[k, n] && k < n, k++]; k, {n, 85}] (* Michael De Vlieger, Sep 21 2015 *)

PROG

(Haskell)

import Data.List (isInfixOf)

a261461 x = f $ tail a030308_tabf where

f (cs:css) = if isInfixOf cs (a030308_row x)

then f css else foldr (\d v -> 2 * v + d) 0 cs

(Python)

from itertools import count

def a(n):

b, k = bin(n)[2:], 1

return next(k for k in count(1) if bin(k)[2:] not in b)

print([a(n) for n in range(86)]) # Michael S. Branicky, Feb 26 2023