

A334594


Irregular table read by rows: T(n,k) is the binary interpretation of the kth row of the XORtriangle with first row generated from the binary expansion of n. 1 <= k <= A070939(n).


7



1, 2, 1, 3, 0, 4, 2, 1, 5, 3, 0, 6, 1, 1, 7, 0, 0, 8, 4, 2, 1, 9, 5, 3, 0, 10, 7, 0, 0, 11, 6, 1, 1, 12, 2, 3, 0, 13, 3, 2, 1, 14, 1, 1, 1, 15, 0, 0, 0, 16, 8, 4, 2, 1, 17, 9, 5, 3, 0, 18, 11, 6, 1, 1, 19, 10, 7, 0, 0, 20, 14, 1, 1, 1, 21, 15, 0, 0, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

An XORtriangle is an inverted 01 triangle formed by choosing a top row and having each entry in the subsequent rows be the XOR of the two values above it.


LINKS



EXAMPLE

Table begins:
1;
2, 1;
3, 0;
4, 2, 1;
5, 3, 0;
6, 1, 1;
7, 0, 0;
8, 4, 2, 1;
9, 5, 3, 0;
10, 7, 0, 0;
11, 6, 1, 1;
For the 11th row, the binary expansion of 11 is 1011_2, and the corresponding XORtriangle is
1 0 1 1
1 1 0
0 1
1
Reading the rows of this triangle in binary gives 11, 6, 1, 1.


MATHEMATICA

Array[Prepend[FromDigits[#, 2] & /@ #2, #1] & @@ {#, Rest@ NestWhileList[Map[BitXor @@ # &, Partition[#, 2, 1]] &, IntegerDigits[#, 2], Length@ # > 1 &]} &, 21] // Flatten (* Michael De Vlieger, May 08 2020 *)


PROG

(PARI) row(n) = {my(b=binary(n), v=vector(#b)); v[1] = n; for (n=1, #b1, b = vector(#b1, k, bitxor(b[k], b[k+1])); v[n+1] = fromdigits(b, 2); ); v; } \\ Michel Marcus, May 08 2020


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



