A214809 - OEIS

%I #27 Jan 16 2024 12:11:48

%S 2,1,0,4,0,3,0,0,1,1,3,1,6,4,0,0,0,4,2,0,1,2,4,2,1,1,0,0,7,0,0,3,0,1,

%T 0,8,1,5,0,0,3,1,0,1,0,0,1,1,4,0,0,1,1,0,0,0,0,3,1,1,2,0,2,2,0,1,5,1,

%U 3,2,0,0,4,0,0,1,2,5,8,6,4,11,3,8,0,0,1,0,6,4,2,1,0,0,2,9,5,1,0,0,2,0,0,3,3,1,5,3,2,7,5,0,4,0,5,0,1,1,2,0

%N A214330 prefixed by a 0 consists of a concatenation of strings 0111010(01)^n, each such string ending with n >= 0 copies of 10; sequence gives successive values of n.

%C If we change the three initial terms of A214551 (as in A214331 and A214626), again read the sequence mod 2, and decompose the result into strings 0111010(01)^n, will the sequence of values of n have anything in common with the current sequence? Is A214809 in any way characteristic of this family of sequences?

%H N. J. A. Sloane, <a href="/A214809/b214809.txt">Table of n, a(n) for n = 1..916</a>

%H N. J. A. Sloane, <a href="/A214330/a214330.jpg">State diagram</a> [State diagram for A214551 mod 2 for any three initial terms. Nodes are labeled with a(n-2) a(n-1) a(n), edges are labeled with a(n+1).]

%e Let s = 0111010. Then 0, A214330 starts

%e s1010s10ss10101010ss101010sss10s10s101010s10s101010101010s10101010ssss101\

%e 01010s1010ss10s1010s10101010s1010s10s10sss10101010101010sss101010ss10ss10\

%e 10101010101010s10s1010101010sss101010s10ss10sss10s10s10101010sss10s10ssss\

%e s101010s10s10s1010ss1010s1010ss10s1010101010s10s101010s1010sss10101010sss\

%e ..., in which the successive numbers of 10's are 2, 1, 0, 4, 0, 3, 0, 0, ...

%o (Shell) # Using b-file for A214330, condense 10000 terms into one long string; prefix with 0.

%o # Using vi, s/0111010/s/g; then s/10/a/g;

%o # Using tr, break up so that there is one s per line.

%o # Using awk, count the a's per line.

%Y Cf. A214330, A214551.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jul 30 2012