A346303 Positions of words in A076478 that start with 0 and end with 0.

1, 3, 7, 9, 15, 17, 19, 21, 31, 33, 35, 37, 39, 41, 43, 45, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179

Offset

1,2

Comments

The sequences A346303, A171757, A346304, A346305 partition the positive integers. See A076478 for a guide to related sequences.

The position of the words 0, 00, 000, 0000, ... (all-zero) in A076478 is given by A000225. So this sequence is given by the subsequence A000225 and filling the gaps halfway up (until the leading 0 toggles) with odd numbers, from 7 to 9, from 15 to 21, from 31 to 45 etc. So the first differences are 2, 4, 2, 6, 2, 2, 2, 10, 2, 2, 2, 2, 2, 2, 2, 18, 2, 2, ... which is A052548 with 1, 3, 7, 15,... (A000225) intermediate 2's. - R. J. Mathar, Sep 08 2021

Links

Table of n, a(n) for n=1..59.

Example

The first fourteen words w(n) are 0, 1, 00, 01, 10, 11, 000, 001, 010, 011, 100, 101, 110, 111, so that a(3) = 7.

Mathematica

(See A007931.)

Crossrefs

Cf. A007931, A076478, A171757, A346304, A346305.

Sequence in context: A118556 A279617 A199919 * A178207 A210532 A110872

Adjacent sequences: A346300 A346301 A346302 * A346304 A346305 A346306

Keyword

nonn,base

Author

Clark Kimberling, Jul 21 2021

Status

approved