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

0,3

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

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

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).

Example

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

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 *)

Prog

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

Crossrefs

Cf. A038554, A038557.

Cf. A053645.

Sequence in context: A181840 A198432 A102391 * A342303 A193508 A307728

Adjacent sequences: A038553 A038554 A038555 * A038557 A038558 A038559

Keyword

nonn,nice,easy,look

Author

N. J. A. Sloane

Extensions

More terms from Naohiro Nomoto, Apr 08 2001

Status

approved