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A261461 a(n) is the smallest nonzero number that is not a substring of n in its binary representation.

%I A261461 #34 Feb 26 2023 16:47:28
%S A261461 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,
%T A261461 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,
%U A261461 3,3,5,5,3,3,3,6,5,7,5,5,3,3,3,6,3,3
%N A261461 a(n) is the smallest nonzero number that is not a substring of n in its binary representation.
%C A261461 A261018(n) = a(A260273(n)).
%C A261461 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
%C A261461 a(A062289(n))=A261922(A062289(n)); a(A126646(n))!=A261922(A126646(n)). - _Reinhard Zumkeller_, Sep 17 2015
%H A261461 Reinhard Zumkeller, <a href="/A261461/b261461.txt">Table of n, a(n) for n = 0..10000</a>
%H A261461 David Consiglio, Jr., <a href="/A261461/a261461.txt">Python Program</a>
%F A261461 a(n) = A144016(n) + 1 for any n > 0. - _Rémy Sigrist_, Mar 10 2018
%t A261461 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 *)
%o A261461 (Haskell)
%o A261461 import Data.List (isInfixOf)
%o A261461 a261461 x = f $ tail a030308_tabf where
%o A261461    f (cs:css) = if isInfixOf cs (a030308_row x)
%o A261461                    then f css else foldr (\d v -> 2 * v + d) 0 cs
%o A261461 (Python)
%o A261461 from itertools import count
%o A261461 def a(n):
%o A261461     b, k = bin(n)[2:], 1
%o A261461     return next(k for k in count(1) if bin(k)[2:] not in b)
%o A261461 print([a(n) for n in range(86)]) # _Michael S. Branicky_, Feb 26 2023
%Y A261461 Cf. A007088, A030308, A260273, A261018; record values and where they occur: A261466, A261467.
%Y A261461 See A261922 for a variant.
%Y A261461 Cf. A062289, A144016, A261922, A126646.
%K A261461 nonn,base
%O A261461 0,2
%A A261461 _Reinhard Zumkeller_, Aug 30 2015