A038556 Periodic derivative of n.

0, 0, 3, 0, 5, 6, 3, 0, 9, 10, 15, 12, 5, 6, 3, 0, 17, 18, 23, 20, 29, 30, 27, 24, 9, 10, 15, 12, 5, 6, 3, 0, 33, 34, 39, 36, 45, 46, 43, 40, 57, 58, 63, 60, 53, 54, 51, 48, 17, 18, 23, 20, 29, 30, 27, 24, 9, 10, 15, 12, 5, 6, 3, 0, 65, 66, 71, 68, 77, 78, 75, 72, 89, 90, 95, 92, 85

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy
• look

Comments

Every term is an evil number (A001969) and every evil number occurs an infinite number of times in this sequence. Observe self-similarity in the graph of the sequence. - T. D. Noe, Jun 22 2007

Examples

			11=1011->1100 so a(11)=12.
		

References

• Simmons, G. J. The structure of the differentiation digraphs of binary sequences. Ars Combin. 35 (1993), A, 71-88. Math. Rev. 95f:05052.

Links

• T. D. Noe, Table of n, a(n) for n=0..4096

Crossrefs

Cf. A038554, A038557.

Cf. A053645.

Programs

Haskell

import Data.Bits (xor)
a038556 n = n `xor` (a053645 $ 2 * n + 1) :: Integer

Mathematica

a[n_] := With[{bits = IntegerDigits[n, 2]}, FromDigits[ Thread[ BitXor[ bits, RotateLeft[bits]]], 2]]; Table[a[n], {n, 0, 76}] (* Jean-François Alcover, Aug 06 2012, from 2nd formula *)

Formula

If n=b_k b_{k-1} ... b_0 in base 2, a(n) is number with binary expansion (b_k+b_{k-1}) (b_{k-1}+b_{k-2}) ... (b_1+b_0) (b_0+b_{k}). Also n XOR (n rotate 1).

Extensions

More terms from Naohiro Nomoto, Apr 08 2001