A308173 - OEIS

A308173

Take the list of all binary vectors (including those beginning with 0) in lexicographic order; a(n) is the index of the first occurrence of the n-th binary vector as a subsequence of A038219.

1, 2, 3, 1, 2, 5, 13, 3, 1, 4, 2, 6, 5, 10, 17, 13, 14, 3, 1, 7, 4, 9, 12, 2, 6, 8, 11, 5, 10, 21, 48, 17, 13, 18, 14, 28, 3, 19, 15, 1, 29, 7, 25, 4, 9, 20, 16, 12, 27, 2, 30, 6, 24, 8, 11, 26, 5, 23, 10, 22, 21, 58, 99, 48, 49, 17, 13, 50, 43, 18, 14, 33, 28

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Ehrenfeucht and Mycielski (1992) prove that every binary vector appears in A038219, so the sequence is well-defined.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..65535

A. Ehrenfeucht and J. Mycielski, A pseudorandom sequence - how random is it?, Amer. Math. Monthly, 99 (1992), 373-375.

EXAMPLE

A038219 begins 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, ... and has offset 1. Here is the start of the list of binary vectors and the index where they first appear in the sequence:

0: 1

1: 2

00: 3

01: 1

10: 2

11: 5

000: 13

001: 3

...

CROSSREFS

Cf. A038219, A253060, A253061.

Sequence in context: A245559 A117488 A307668 * A256910 A181176 A131108