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

1,2

Comments

The position 1 corresponds to the most significant bit.

Links

Paul Tek, Table of n, a(n) for n = 1..3321

Paul Tek, PARI program for this sequence

Formula

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

Example

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.

Prog

(PARI) See Link section.

Crossrefs

Cf. A098645.

Sequence in context: A122039 A083706 A352667 * A261983 A074896 A015713

Adjacent sequences: A229069 A229070 A229071 * A229073 A229074 A229075

Keyword

nonn,base

Author

Paul Tek, Sep 12 2013

Status

approved