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%I #10 Apr 04 2015 21:34:04
%S 2,3,30,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,56,57,63,330,333,
%T 3333,33333,33400,40300,40400,40401,40402,40404,40405,40406,40407,
%U 40408,40409,40410,40411,40412,40414,40415,40416,40417,40418,40419,40420
%N Smallest sequence which lists the position of digits "3" in the sequence.
%C 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 We cannot have a(1)=1 (since then there's no "3" in the first place), but a(1)=2 is possible.
%e Then a(2)=3 is a possible choice and certainly the smallest.
%e This "predicts" that a(3) starts with a digit "3", so a(3)=30 is the smallest possible choice.
%e 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 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 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 The terms a(5)=41, a(6)=42 leave 330 as the smallest possible choice for the next term.
%e 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 (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 Cf. A098645, A167519, A167520, A167452.
%K base,nonn
%O 1,1
%A _M. F. Hasler_, Nov 19 2009
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