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

0,3

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.

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

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

Sequence in context: A328841 A276008 A331171 * A193917 A089135 A215412

Adjacent sequences: A336950 A336951 A336952 * A336954 A336955 A336956

Keyword

nonn,base,look

Author

Gage Schacher, Aug 08 2020

Status

approved