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A333921 a(n) is the least k such that the decimal representation of n appears as a substring in the concatenation of 0, 1, ..., k.

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%I A333921 #10 Apr 12 2020 13:57:36
%S A333921 0,1,2,3,4,5,6,7,8,9,10,11,2,13,14,15,16,17,18,19,20,13,22,3,24,25,26,
%T A333921 27,28,29,30,14,24,33,4,35,36,37,38,39,40,15,25,35,44,5,46,47,48,49,
%U A333921 50,16,26,36,46,55,6,57,58,59,60,17,27,37,47,57,66,7,68
%N A333921 a(n) is the least k such that the decimal representation of n appears as a substring in the concatenation of 0, 1, ..., k.
%C A333921 Every nonnegative integer appears finitely many times in this sequence.
%H A333921 Rémy Sigrist, <a href="/A333921/b333921.txt">Table of n, a(n) for n = 0..10000</a>
%F A333921 a(n) <= n with equality iff n = 0 or n belongs to A131881.
%F A333921 a(A007908(n)) = n for any n > 0.
%o A333921 (PARI) a(n, base=10) = { my (w=base^#digits(n, base), m=0); for (k=0, oo, my (d=if (k, digits(k, base), [0])); for (i=1, #d, m=(base*m+d[i])%w; if (m==n, return (k)))) }
%Y A333921 Cf. A007908, A116700, A131881, A333920 (binary variant).
%K A333921 nonn,base
%O A333921 0,3
%A A333921 _Rémy Sigrist_, Apr 10 2020