cp's OEIS Frontend

A167453 Smallest sequence which lists the position of digits "3" in the sequence.

%I A167453 #10 Apr 04 2015 21:34:04
%S A167453 2,3,30,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,56,57,63,330,333,
%T A167453 3333,33333,33400,40300,40400,40401,40402,40404,40405,40406,40407,
%U A167453 40408,40409,40410,40411,40412,40414,40415,40416,40417,40418,40419,40420
%N A167453 Smallest sequence which lists the position of digits "3" in the sequence.
%C A167453 The lexicographically earliest sequence such that a(1),a(2),a(3),... is the (increasing) list of the positions of digits "3" in the string obtained by concatenating all these terms, written in base 10.
%e A167453 We cannot have a(1)=1 (since then there's no "3" in the first place), but a(1)=2 is possible.
%e A167453 Then a(2)=3 is a possible choice and certainly the smallest.
%e A167453 This "predicts" that a(3) starts with a digit "3", so a(3)=30 is the smallest possible choice.
%e A167453 The next digit "3" must not appear until the 30th digit of the sequence, so we fill in terms 40,41,42,44,45... (omitting 43 which has a digit "3").
%e A167453 Now it happens that the term 53 would correspond to digits # 29 and 30=a(3) of the sequence, so we can simply continue with this and 4 more terms, up to 57.
%e A167453 The next term must have its second digit (digit # 40=a(4) of the sequence) equal to 3, so 63 is the smallest choice.
%e A167453 The terms a(5)=41, a(6)=42 leave 330 as the smallest possible choice for the next term.
%e A167453 The terms 44,45,46 and 47,48,49,50 and 51,52,53,54,55 lead to the subsequent terms 333, 3333, 33333.
%o A167453 (PARI) concat([[2,3,30],vector((40-4)/2-1,i,40-(i<=3)+i), [63, 330, 333, 3333, 33333, 33400,40300], select(x->x%10-3 & x\10%10-3,vector((330-63)\5+10,i,40400+i-1)) ])
%Y A167453 Cf. A098645, A167519, A167520, A167452.
%K A167453 base,nonn
%O A167453 1,1
%A A167453 _M. F. Hasler_, Nov 19 2009