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.

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

Author

Paul Tek, Sep 12 2013

Keywords

• nonn
• base

Comments

The position 1 corresponds to the most significant bit.

Examples

			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.
		

Links

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

Crossrefs

Cf. A098645.

Programs

PARI

See Link section.

Formula

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