A167452 Smallest sequence which lists the position of digits "2" in the sequence.

3, 4, 22, 30, 31, 33, 34, 35, 36, 37, 38, 42, 43, 44, 45, 52, 202, 222, 223, 302, 2220, 3000, 3200, 3300, 3301, 3303, 3304, 3305, 3306, 3307, 3308, 3309, 3310, 3311, 3313, 3314, 3315, 3316, 3317, 3318, 3319, 3330, 3331, 3333, 3334, 3335, 3336, 3337, 3338

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.

Links

Table of n, a(n) for n=1..49.

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 the 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

Cf. A098645, A167519, A167520.

Sequence in context: A012255 A012247 A057791 * A375958 A316192 A122660

Adjacent sequences: A167449 A167450 A167451 * A167453 A167454 A167455

Keyword

base,nonn,nice

Author

M. F. Hasler, Nov 19 2009

Status

approved