

A334593


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


6



1, 2, 2, 3, 4, 4, 3, 4, 6, 5, 7, 5, 7, 6, 4, 5, 8, 9, 8, 8, 7, 10, 9, 7, 8, 9, 10, 8, 9, 8, 5, 6, 10, 10, 12, 12, 12, 10, 12, 10, 12, 8, 12, 12, 14, 12, 12, 8, 12, 12, 10, 12, 12, 14, 12, 10, 12, 12, 12, 10, 12, 10, 6, 7, 12, 14, 13, 12, 15, 15, 16, 14, 17, 15
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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.
Records occur at 1, 2, 4, 5, 9, 11, 17, 18, 22, 35, 45, 69, 71, 73, 91, 139, 142, 146, 182, ...


LINKS



FORMULA



EXAMPLE

For n = 53, a(53) = 12 because 53 = 110101_2 in binary, and the corresponding XORtriangle has 12 ones:
1 1 0 1 0 1
0 1 1 1 1
1 0 0 0
1 0 0
1 0
1


MATHEMATICA

Array[Total@ Flatten@ NestWhileList[Map[BitXor @@ # &, Partition[#, 2, 1]] &, IntegerDigits[#, 2], Length@ # > 1 &] &, 74] (* Michael De Vlieger, May 08 2020 *)


PROG

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


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



