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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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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 A213724

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

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Last modified April 19 19:16 EDT 2014. Contains 240777 sequences.