

A038556


Periodic derivative of n.


4



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
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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 selfsimilarity 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, 7188. Math. Rev. 95f:05052.


LINKS

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


FORMULA

If n=b_k b_{k1} ... b_0 in base 2, a(n) is number with binary expansion (b_k+b_{k1}) (b_{k1}+b_{k2}) ... (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}] (* JeanFrançois 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 * A193508 A052483 A249859
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



