A383848 -id:A383848 - cp's OEIS frontend

A383850 Fixed points of A383848 and A383849.

0, 1, 3, 7, 10, 15, 31, 63, 127, 153, 170, 204, 255, 292, 365, 438, 511, 1023, 2047, 2275, 2405, 2470, 2665, 2730, 2860, 3185, 3250, 3380, 3640, 4095, 8191, 16383, 32767, 34695, 34952, 35723, 36237, 36494, 37779, 38293, 38550, 39321, 39578, 40092, 41891, 42405, 42662, 43433, 43690

Offset: 1

Paolo Xausa, May 13 2025

Cf. A383848, A383849.

A000225 is a subsequence.

A383850Q[k_] := # == RotateLeft[#, Total[#]]& [IntegerDigits[k, 2]];
Select[Range[0, 50000], A383850Q]

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

A383850 Fixed points of A383848 and A383849.

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