A167455 Smallest sequence which lists the position of digits "5" in the sequence.

2, 5, 6, 7, 55, 56, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 550, 605, 5555, 6555, 55555, 56555, 555555, 600000, 600001, 600002, 600003, 600004, 600006, 600007, 600008, 600009, 600010, 600011, 600012, 600013

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 "5" 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 "5" in the first place), but a(1)=2 is possible.
Then a(2) must start with a digit "5", so a(2)=5 is the smallest possible choice.
This allows us to go on with a(3)=6, a(4)=6, but then must be follow 3 digits "5" (the 5th, 6th and 7th digit of the sequence), so a(5)=55 and a(6)=56 are the smallest possible choice.
The reasoning continues in analogy with A167452-A167454.

Prog

(PARI) concat([ [2, 5, 6, 7, 55, 56], vector((55-8)\2, i, 60-(i<=5)+i+(i>=15)), [550, 605, 5555, 6555, 55 555, 56 555, 555 555], select(x->x%10-5 & x\10%10-5, vector((550-84)\6+10, i, 600 000+i-1)) ])

Crossrefs

Cf. A098645, A167519, A167520, A167452, A167453, A167454.

Sequence in context: A344865 A350130 A033959 * A159752 A352325 A228089

Adjacent sequences: A167452 A167453 A167454 * A167456 A167457 A167458

Keyword

base,nonn

Author

M. F. Hasler, Nov 19 2009

Status

approved