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.

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

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[i-1]=="1" and x[i]=="0":
............s+=i
....return s

Crossrefs

Cf. A003188, A014550, A049502, A281388.

Sequence in context: A353310 A347883 A024712 * A198243 A164965 A021823

Adjacent sequences: A281494 A281495 A281496 * A281498 A281499 A281500

Keyword

nonn,base

Author

Indranil Ghosh, Jan 23 2017

Status

approved