

A334592


Number of zeros in XORtriangle with first row generated from the binary expansion of n.


6



0, 1, 1, 3, 2, 2, 3, 6, 4, 5, 3, 5, 3, 4, 6, 10, 7, 6, 7, 7, 8, 5, 6, 8, 7, 6, 5, 7, 6, 7, 10, 15, 11, 11, 9, 9, 9, 11, 9, 11, 9, 13, 9, 9, 7, 9, 9, 13, 9, 9, 11, 9, 9, 7, 9, 11, 9, 9, 9, 11, 9, 11, 15, 21, 16, 14, 15, 16, 13, 13, 12, 14, 11, 13, 12, 17, 12
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OFFSET

1,4


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.
Conjecture: Records occur at powers of two.


LINKS



FORMULA



EXAMPLE

For n = 53, a(53) = 9 because 53 = 110101_2 in binary, and the corresponding XORtriangle has 9 zeros:
1 1 0 1 0 1
0 1 1 1 1
1 0 0 0
1 0 0
1 0
1


MATHEMATICA

Array[Count[Flatten@ NestWhileList[Map[BitXor @@ # &, Partition[#, 2, 1]] &, IntegerDigits[#, 2], Length@ # > 1 &], 0] &, 77] (* Michael De Vlieger, May 08 2020 *)


PROG

(PARI) a(n) = {my(b=binary(n), nb=#bhammingweight(n)); for (n=1, #b1, b = vector(#b1, k, bitxor(b[k], b[k+1])); nb += #bvecsum(b); ); nb; } \\ Michel Marcus, May 08 2020


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



