cp's OEIS Frontend

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 A308173 #19 May 21 2019 11:54:51
%S A308173 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 A308173 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 A308173 26,5,23,10,22,21,58,99,48,49,17,13,50,43,18,14,33,28
%N 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.
%C A308173 Ehrenfeucht and Mycielski (1992) prove that every binary vector appears in A038219, so the sequence is well-defined.
%H A308173 Rémy Sigrist, <a href="/A308173/b308173.txt">Table of n, a(n) for n = 1..65535</a>
%H A308173 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 A308173 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 A308173 0: 1
%e A308173 1: 2
%e A308173 00: 3
%e A308173 01: 1
%e A308173 10: 2
%e A308173 11: 5
%e A308173 000: 13
%e A308173 001: 3
%e A308173 ...
%Y A308173 Cf. A038219, A253060, A253061.
%K A308173 nonn
%O A308173 1,2
%A A308173 _N. J. A. Sloane_, May 20 2019
%E A308173 More terms from _Rémy Sigrist_, May 21 2019