A383850 -id:A383850 - cp's OEIS frontend

A383848 In the binary representation of n, rotate left by the number of ones.

0, 1, 1, 3, 1, 6, 3, 7, 1, 6, 10, 13, 3, 14, 7, 15, 1, 6, 10, 28, 18, 13, 21, 27, 3, 14, 22, 29, 7, 30, 15, 31, 1, 6, 10, 28, 18, 44, 52, 57, 34, 13, 21, 58, 37, 27, 43, 55, 3, 14, 22, 60, 38, 29, 45, 59, 7, 30, 46, 61, 15, 62, 31, 63, 1, 6, 10, 28, 18, 44, 52, 120, 34

Offset: 0

Paolo Xausa, May 13 2025

Equivalently, rotate right by the number of zeros.

			a(19) = 28 because 19 = 10011_2, and 10011_2 rotated to the left 3 times gives 11100_2 = 28.

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

Cf. A006257, A007088, A383849, A383850 (fixed points).

A383848[n_] := FromDigits[RotateLeft[#, Total[#]], 2] & [IntegerDigits[n, 2]];
Array[A383848,100,0]

A383849 In the binary representation of n, rotate right by the number of ones.

Original entry on oeis.org

0, 1, 1, 3, 2, 3, 5, 7, 4, 6, 10, 7, 3, 11, 13, 15, 8, 12, 20, 14, 5, 22, 26, 15, 6, 7, 11, 23, 19, 27, 29, 31, 16, 24, 40, 28, 9, 44, 52, 30, 10, 13, 21, 46, 37, 54, 58, 31, 12, 14, 22, 15, 38, 23, 27, 47, 7, 39, 43, 55, 51, 59, 61, 63, 32, 48, 80, 56, 17, 88, 104, 60, 18

Offset: 0

Paolo Xausa, May 13 2025

Equivalently, rotate left by the number of zeros.

			a(19) = 14 because 19 = 10011_2, and 10011_2 rotated to the right 3 times gives 01110_2 = 14.

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

Cf. A007088, A038572, A383848, A383850 (fixed points).

A383849[n_] := FromDigits[RotateRight[#, Total[#]], 2] & [IntegerDigits[n, 2]];
Array[A383849, 100, 0]

cp's OEIS Frontend

A383848 In the binary representation of n, rotate left by the number of ones.

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