cp's OEIS Frontend

A167519 Lexicographically earliest increasing sequence which lists the positions of the zero digits in the sequence.

%I A167519 #15 Oct 09 2024 09:11:27
%S A167519 3,10,11,12,11000,11111,11112,11113,11114,11115,11116,11117,11118,
%T A167519 11119,11121,11122,11123,11124,11125,11126,11127,11128,11129,11131,
%U A167519 11132,11133,11134,11135,11136,11137,11138,11139,11141,11142,11143,11144
%N A167519 Lexicographically earliest increasing sequence which lists the positions of the zero digits in the sequence.
%C A167519 The terms of the sequence give the positions of the digits '0' in the string formed by concatenating all the terms (written in base 10).
%e A167519 The sequence cannot start with 1 (which would mean it starts with 0) or 2 (which would mean that the second term equals 0), so a(1)=3 is the smallest possibility.
%e A167519 Thereafter, the smallest possible value for a(2), which must have '0' as second digit, is a(2)=10.
%e A167519 This means that the next digit '0' must occur at position 10; up to there, we use the smallest possible values for a(3)=11 and a(4)=12.
%e A167519 Then must follow two nonzero digits (which must be part of a(5)) and then three zero digits (from a(2),a(3),a(4) = 10, 11, 12). None of the latter can be the first digit of a(6), so they must be part of a(5), for which the smallest possibility is therefore a(5)=11000.
%e A167519 This also means that there is no digit '0' between the 12th digit (= the last digit of a(6)), and the 11000th digit of the sequence. So there follow roughly 11000/5 terms which are the smallest possible 5-digit terms without a zero digit.
%Y A167519 Cf. A167500-A167503. See A210414 for another version.
%K A167519 nonn,base
%O A167519 1,1
%A A167519 _M. F. Hasler_, Nov 05 2009
%E A167519 Edited by _Charles R Greathouse IV_, Apr 24 2010
%E A167519 Definition corrected by _Jaroslav Krizek_, Jun 19 2014