

A281497


Write n in binary reflected Gray code and sum the positions where there is a '1' followed immediately to the left by a '0', counting the rightmost digit as position 1.


2



0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 1, 0, 0, 1, 2, 2, 0, 0, 1, 0, 3, 4, 3, 3, 2, 2, 1, 0, 0, 1, 2, 2, 3, 3, 4, 3, 0, 1, 0, 0, 2, 2, 1, 0, 4, 5, 6, 6, 4, 4, 5, 4, 3, 4, 3, 3, 2, 2, 1, 0, 0, 1, 2, 2, 3, 3, 4, 3, 4, 5, 4, 4, 6, 6, 5, 4, 0, 1, 2, 2, 0, 0, 1, 0, 3, 4, 3, 3, 2, 2, 1, 0, 5, 6, 7, 7, 8, 8, 9, 8, 5, 6, 5, 5, 7, 7, 6
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OFFSET

1,12


LINKS

Indranil Ghosh, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A049502(A003188(n)).


EXAMPLE

For n = 12, the binary reflected Gray code for 12 is '1010'. In '1010', the position of '1' followed immediately to the left by a '0' counting from right is 2. So, a(12) = 2.


MATHEMATICA

Table[If[Length@ # == 0, 0, Total[#[[All, 1]]]] &@ SequencePosition[ Reverse@ IntegerDigits[#, 2] &@ BitXor[n, Floor[n/2]], {1, 0}], {n, 120}] (* Michael De Vlieger, Jan 23 2017, Version 10.1, after Robert G. Wilson v at A003188 *)


PROG

(Python)
def G(n):
....return bin(n^(n/2))[2:]
def a(n):
....x=G(n)[::1]
....s=0
....for i in range(1, len(x)):
........if x[i1]=="1" and x[i]=="0":
............s+=i
....return s


CROSSREFS

Cf. A003188, A014550, A049502, A281388.
Sequence in context: A283988 A276204 A024712 * A198243 A164965 A021823
Adjacent sequences: A281494 A281495 A281496 * A281498 A281499 A281500


KEYWORD

nonn,base


AUTHOR

Indranil Ghosh, Jan 23 2017


STATUS

approved



