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.

%I #19 May 21 2019 11:54:51

%S 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,

%T 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,

%U 26,5,23,10,22,21,58,99,48,49,17,13,50,43,18,14,33,28

%N 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.

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

%H Rémy Sigrist, <a href="/A308173/b308173.txt">Table of n, a(n) for n = 1..65535</a>

%H A. Ehrenfeucht and J. Mycielski, <a href="http://www.jstor.org/stable/2324917">A pseudorandom sequence - how random is it?</a>, Amer. Math. Monthly, 99 (1992), 373-375.

%e 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:

%e 0: 1

%e 1: 2

%e 00: 3

%e 01: 1

%e 10: 2

%e 11: 5

%e 000: 13

%e 001: 3

%e ...

%Y Cf. A038219, A253060, A253061.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, May 20 2019

%E More terms from _Rémy Sigrist_, May 21 2019