A366140 -id:A366140 - cp's OEIS frontend

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

Gage Schacher, Aug 08 2020

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.

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

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

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

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

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

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

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

A366139 In binary representation, rotate the digits of n left n places.

Original entry on oeis.org

0, 1, 2, 3, 1, 6, 6, 7, 8, 3, 10, 13, 12, 11, 11, 15, 1, 6, 20, 25, 20, 11, 26, 29, 12, 25, 21, 15, 7, 30, 30, 31, 2, 12, 40, 49, 36, 11, 26, 60, 10, 52, 42, 23, 50, 45, 43, 55, 48, 35, 11, 30, 13, 58, 54, 47, 35, 15, 46, 61, 60, 59, 59, 63, 1, 6, 20, 56, 17, 98

Offset: 0

Paolo Xausa, Sep 30 2023

			a(4) = 1 because 4 in base 2 is 100 and 100 rotated left 4 times is 100 -> 001 -> 010 -> 100 -> 001 = 1.
a(5) = 6 because 5 in base 2 is 101 and 101 rotated left 5 times is 101 -> 011 -> 110 -> 101 -> 011 -> 110 = 6 in base 10.

Paolo Xausa, Table of n, a(n) for n = 0..16383

Cf. A006257, A007088, A366140 (fixed points).

Cf. A336953 (rotate right).

A366139[n_]:=FromDigits[RotateLeft[IntegerDigits[n,2],n],2];
Array[A366139,100,0]

def A366139(n): return int((s:=bin(n))[(m:=n%n.bit_length()+2):]+s[2:m],2) if n else 0 # Chai Wah Wu, Oct 03 2023

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python