A098645 -id:A098645 - cp's OEIS frontend

A167456 Smallest sequence which lists the position of digits "6" in the sequence.

2, 6, 7, 8, 9, 66, 660, 700, 701, 702, 703, 704, 705, 707, 708, 709, 710, 711, 712, 713, 714, 715, 717, 718, 719, 760, 770, 771, 772, 773, 774, 775, 777, 778, 779, 780, 781, 782, 783, 784, 785, 787, 788, 789, 790, 791, 792, 793, 794, 795, 797, 798, 799, 800

Offset: 1

M. F. Hasler, Nov 19 2009

The lexicographically earliest sequence such that a(1),a(2),a(3),... is the (increasing) list of the positions of digits "6" in the string obtained by concatenating all these terms, written in base 10.

			We cannot have a(1)=1 (since then there's no "6" in the first place), but a(1)=2 is possible.
Then a(2) must start with a digit "6", so a(2)=6 is the smallest possible choice.
This allows us to go on with a(3)=7, a(4)=8, a(5)=9, but then must be follow 4 digits "6" (the 6th through 9th digit of the sequence), so a(6)=66 and a(7)=660 are the smallest possible choices.
Then the reasoning continues in analogy with A167452-A167455.

Cf. A098645, A167519, A167520, A167452 - A167455.

concat([ [2,6,7,8,9,66,660], vector((66-9)\3-1,i,700-(i<=6)+i+(i>=16)), [760], select(x->x%10-6 & x\10%10-6,vector((660-66)\3+10,i,770+i-1)) ])

A229072 Lexicographically earliest sequence of distinct natural numbers such that, for any number n in the sequence, the positions of the 1's in the binary representation of n are in the sequence, whereas the positions of the 0's are not.

Original entry on oeis.org

1, 4, 9, 18, 36, 72, 144, 289, 578, 1156, 2312, 4624, 9248, 18496, 36992, 73984, 147969, 295938, 591876, 1183752, 2367504, 4735008, 9470016, 18940032, 37880064, 75760128, 151520256, 303040512, 606081024, 1212162048, 2424324096, 4848648192, 9697296384

Offset: 1

Paul Tek, Sep 12 2013

The position 1 corresponds to the most significant bit.

			1 has a 1 at position 1, and no 0's, hence 1 belongs to the sequence.
2 has a 0 at position 2, hence 2 cannot belong to the sequence.
3 has a 1 at position 2, as 2 cannot belong to the sequence, 3 cannot either.
4 has a 1 at position 1, and 0's at positions 2 and 3, hence 4 belongs to the sequence.
9 has 1's at positions 1 and 4, and 0's at positions 2 and 3, hence 9 belongs to the sequence.

Paul Tek, Table of n, a(n) for n = 1..3321
Paul Tek, PARI program for this sequence

Cf. A098645.

PARI
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See Link section.
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a(n) = Sum_{a(i) <= n+1} 2^(n+1-a(i)), for any n>1, with a(1)=1.

cp's OEIS Frontend

A167456 Smallest sequence which lists the position of digits "6" in the sequence.

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