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

2, 3, 30, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 63, 330, 333, 3333, 33333, 33400, 40300, 40400, 40401, 40402, 40404, 40405, 40406, 40407, 40408, 40409, 40410, 40411, 40412, 40414, 40415, 40416, 40417, 40418, 40419, 40420

Offset: 1

Author

M. F. Hasler, Nov 19 2009

Keywords

• base
• nonn

Comments

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.

Examples

			We cannot have a(1)=1 (since then there's no "3" in the first place), but a(1)=2 is possible.
Then a(2)=3 is a possible choice and certainly the smallest.
This "predicts" that a(3) starts with a digit "3", so a(3)=30 is the smallest possible choice.
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").
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.
The next term must have its second digit (digit # 40=a(4) of the sequence) equal to 3, so 63 is the smallest choice.
The terms a(5)=41, a(6)=42 leave 330 as the smallest possible choice for the next term.
The terms 44,45,46 and 47,48,49,50 and 51,52,53,54,55 lead to the subsequent terms 333, 3333, 33333.
		

Crossrefs

Cf. A098645, A167519, A167520, A167452.

Programs

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)) ])