A071858 (Number of 1's in binary expansion of n) mod 3.
0, 1, 1, 2, 1, 2, 2, 0, 1, 2, 2, 0, 2, 0, 0, 1, 1, 2, 2, 0, 2, 0, 0, 1, 2, 0, 0, 1, 0, 1, 1, 2, 1, 2, 2, 0, 2, 0, 0, 1, 2, 0, 0, 1, 0, 1, 1, 2, 2, 0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 2, 2, 0, 1, 2, 2, 0, 2, 0, 0, 1, 2, 0, 0, 1, 0, 1, 1, 2, 2, 0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 2, 2, 0, 2, 0, 0, 1, 0, 1, 1, 2, 0
Offset: 0
References
- J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..10000
- Jin Chen, Zhixiong Wen, Wen Wu, On the additive complexity of a Thue-Morse like sequence, arXiv:1802.03610 [math.CO], 2018.
- Index entries for sequences that are fixed points of mappings
Crossrefs
Programs
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Mathematica
f[n_] := Mod[ Count[ IntegerDigits[n, 2], 1], 3]; Table[ f[n], {n, 0, 104}] (* Or *) Nest[ Flatten[ # /. {0 -> {0, 1}, 1 -> {1, 2}, 2 -> {2, 0}}] &, {0}, 7] (* Robert G. Wilson v Mar 03 2005, modified May 17 2014 *) Table[Mod[DigitCount[n,2,1],3],{n,0,110}] (* Harvey P. Dale, Jul 01 2015 *) -
PARI
for(n=1,200,print1(sum(i=1,length(binary(n)), component(binary(n),i))%3,","))
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PARI
map(d)=if(d==2,[2,0],if(d==1,[1,2],[0,1])) {m=53;v=[];w=[0];while(v!=w,v=w;w=[];for(n=1,min(m,length(v)),w=concat(w,map(v[n]))));for(n=1,2*m,print1(v[n],","))} \\ Klaus Brockhaus, Jun 23 2004
Formula
Recurrence: a(2*n) = a(n), a(2*n+1) = (a(n)+1) mod 3.
a(n) = A000695(n) mod 3. - John M. Campbell, Jul 16 2016
Extensions
Edited by Ralf Stephan, Dec 11 2004
Comments