A336953 In binary representation, rotate the digits of n right n places.

0, 1, 2, 3, 2, 3, 6, 7, 8, 12, 10, 7, 12, 14, 11, 15, 8, 12, 10, 7, 20, 26, 21, 30, 17, 25, 13, 30, 19, 27, 30, 31, 8, 12, 10, 7, 36, 50, 41, 60, 34, 19, 42, 53, 11, 45, 58, 31, 48, 56, 44, 30, 19, 43, 54, 59, 14, 15, 43, 55, 60, 62, 47, 63, 32, 48, 40, 28

Offset: 0

Author

Gage Schacher, Aug 08 2020

Keywords

• nonn
• base
• look

Comments

On the graph, there are a series of larger and larger parallelograms joined together by a straight line on y=x where n is unchanged, mostly in the case where n is a multiple of the bit length of n. In addition to the main line that cuts through the graph, each parallelogram has the same few sloped lines in its borders.

Examples

			a(3) = a('11') = '11' = 3;
a(4) = a('100') = '010' = '10' = 2;
a(5) = a('101') = '011' = '11' = 3;
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..16384

Crossrefs

Cf. A007088, A038572 (rotated one binary place to the right).

Cf. A366139 (rotate left), A366140 (fixed points).

Programs

Mathematica

Array[FromDigits[RotateRight[IntegerDigits[#, 2], #], 2] &, 68, 0] (* Michael De Vlieger, Oct 05 2020 *)

PARI

a(n) = my(d=binary(n)); for (k=1, n, d = concat(d[#d], d[1..#d-1])); fromdigits(d, 2); \\ Michel Marcus, Aug 09 2020

Python

def A336953(n):
    if n == 0: return 0
    l, m = -(n%n.bit_length()), bin(n)[2:]
    return int(m[l:]+m[:l],2) # Chai Wah Wu, Jan 22 2023