OFFSET
1,1
COMMENTS
The lexicographically earliest sequence such that a(1),a(2),a(3),... is the (increasing) list of the positions of digits "1" in the string obtained by concatenating all these terms, written in base 10.
EXAMPLE
We cannot have a(1)=1 (since then there's no 2 in the first place), nor a(1)=2 (since then the first occurrence of a "2" would be at position 1).
But a(1)=3 is possible, "predicting" that the first occurrence of a digit "2" will be in the 3rd digit.
Then a(2)=4 is the smallest possible choice for a(2).
The next two digits (= the 3rd and 4th digit of the sequence) must be a "2", in view of a(1) and a(2). Thus a(3)=22 is the smallest possible choice.
This means that the next digit "2" will occur as the 22nd digit of the sequence, so the following terms are the least possible numbers without digit "2": 30,31,33,...,38. These make up digits 5 to 20 of the sequence.
The following number must have a "2" as second digit, the smallest possibility is 42.
PROG
(PARI) concat([ [3, 4, 22], vector((22-4)/2-1, i, i+30-(i<=2)), vector(4, i, 42+i-1), [52, 202, 222, 223, 302, 2220, 3000, 3200], select(x -> x%10-2 & x\10%10-2 & x\100%10-2, vector((202-52)\4+13, i, 3300+i-1)) ])
CROSSREFS
KEYWORD
base,nonn,nice
AUTHOR
M. F. Hasler, Nov 19 2009
STATUS
approved