A068053 - OEIS

A068053

Start with one 1 in the infinite vector of zeros, shift one right or left and sum mod 2 (bitwise-XOR) to get 11, then shift two steps and XOR to get 1111, then three steps and XOR to get 1110111, then four steps and so on.

%I #13 Mar 09 2024 08:20:30

%S 1,11,1111,1110111,11100000111,1110011111100111,

%T 1110010001111000100111,11100101101100000110110100111,

%U 1110010101010101110111010101010100111,1110010100100111011101111011101110010010100111

%N Start with one 1 in the infinite vector of zeros, shift one right or left and sum mod 2 (bitwise-XOR) to get 11, then shift two steps and XOR to get 1111, then three steps and XOR to get 1110111, then four steps and so on.

%H Paolo Xausa, <a href="/A068053/b068053.txt">Table of n, a(n) for n = 0..44</a>

%p map(convert, A068052,binary);

%t Map[FromDigits[IntegerDigits[#, 2]] &, FoldList[BitXor[#, #*#2] &, 1, 2^Range[10]]] (* _Paolo Xausa_, Mar 07 2024 *)

%Y Sequence A068052 converted to binary. Rows of A053632 reduced mod 2 and concatenated.

%K nonn,base

%O 0,2

%A _Antti Karttunen_, Feb 13 2002