A281553 Write n in binary reflected Gray code, rotate one binary place to the right and convert the code back to decimal.

0, 1, 3, 1, 3, 7, 6, 2, 6, 14, 15, 7, 5, 13, 12, 4, 12, 28, 29, 13, 15, 31, 30, 14, 10, 26, 27, 11, 9, 25, 24, 8, 24, 56, 57, 25, 27, 59, 58, 26, 30, 62, 63, 31, 29, 61, 60, 28, 20, 52, 53, 21, 23, 55, 54, 22, 18, 50, 51, 19, 17, 49, 48, 16, 48, 112, 113, 49, 51, 115, 114, 50, 54, 118

Offset: 0

Author

Indranil Ghosh, Jan 24 2017

Keywords

• nonn
• base

Comments

a(n) = A003188(n), iff the Elias delta code for n contains all 1's without any zeros (see the example section).

Examples

			For n = 5, the binary reflected Gray code for n is '111'. Rotating one binary place to the right , '111' gives back '111' again. 111_2 = 7_10. So, a(5) = 7. (For n = 5, A003188(n) = 7).
For n = 15, the binary reflected Gray code for n is '1000'. Rotating one binary place to the right, '1000' gives '0100'. 100_2 = 4_10. So, a(15) = 4.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A003188, A014550, A038572.

Programs

Python

def rotation(n):
    x=bin(n^(n/2))[2:]
    return int(x[-1]+x[:-1],2)