A167457 Smallest sequence which lists the position of digits "7" in the sequence.

2, 7, 8, 9, 10, 77, 770, 800, 801, 802, 803, 804, 805, 806, 808, 809, 810, 811, 812, 813, 814, 815, 816, 818, 819, 820, 821, 822, 827, 828, 829, 830, 831, 832, 833, 834, 835, 836, 838, 839, 840, 841, 842, 843, 844, 845, 846, 848, 849, 850, 851, 852, 853, 854

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 "7" in the string obtained by concatenating all these terms, written in base 10.

Links

Table of n, a(n) for n=1..54.

Example

We cannot have a(1)=1 (since then there's no "7" in the first place), but a(1)=2 is possible.
Then a(2) must start with a digit "7", so a(2)=7 is the smallest possible choice.
This allows us to go on with a(3)=8, a(4)=9, a(5)=10, but then must be follow 4 digits "6" (the 7th through 10th digit of the sequence), so a(6)=77 and a(7)=770 are the smallest possible choices.
Then the reasoning continues in analogy with A167452-A167456.

Prog

(PARI) concat([ [2, 7, 8, 9, 10, 77, 770], vector((77-10)\3-1, i, 800-(i<=7)+i+(i>=17)), [827], select(x->x%10-7 & x\10%10-7, vector((770-77)\3+20, i, 827+i)) ])

Crossrefs

Cf. A098645, A167519, A167520, A167452 - A167456.

Sequence in context: A047527 A064517 A270804 * A287515 A260581 A179772

Adjacent sequences: A167454 A167455 A167456 * A167458 A167459 A167460

Keyword

base,nonn

Author

M. F. Hasler, Nov 19 2009

Status

approved