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%I #16 Jul 25 2015 20:17:44
%S 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,
%T 12,5,6,3,0,33,34,39,36,45,46,43,40,57,58,63,60,53,54,51,48,17,18,23,
%U 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
%N Periodic derivative of n.
%C 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
%D Simmons, G. J. The structure of the differentiation digraphs of binary sequences. Ars Combin. 35 (1993), A, 71-88. Math. Rev. 95f:05052.
%H T. D. Noe, <a href="/A038556/b038556.txt">Table of n, a(n) for n=0..4096</a>
%F 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).
%e 11=1011->1100 so a(11)=12.
%t 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 *)
%o (Haskell)
%o import Data.Bits (xor)
%o a038556 n = n `xor` (a053645 $ 2 * n + 1) :: Integer
%Y Cf. A038554, A038557.
%Y Cf. A053645.
%K nonn,nice,easy,look
%O 0,3
%A _N. J. A. Sloane_
%E More terms from _Naohiro Nomoto_, Apr 08 2001
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