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A039972 An example of a d-perfect sequence: a(n) = A007317(n) mod 3.

%I A039972 #20 Jul 08 2025 22:41:22
%S A039972 1,2,2,0,0,2,2,1,1,0,0,0,0,0,0,0,0,2,2,1,1,0,0,1,1,2,2,0,0,0,0,0,0,0,
%T A039972 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,1,1,0,0,1,1,2,2,0,0,0,0,0,
%U A039972 0,0,0,1,1,2,2,0,0,2,2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A039972 An example of a d-perfect sequence: a(n) = A007317(n) mod 3.
%C A039972 Odd bisection seems to be A006996. See also A039969. - _Antti Karttunen_, Aug 15 2017
%H A039972 Antti Karttunen, <a href="/A039972/b039972.txt">Table of n, a(n) for n = 1..6561</a>
%H A039972 D. Kohel, S. Ling and C. Xing, <a href="http://www.maths.usyd.edu.au/u/kohel/doc/perfect.ps">Explicit Sequence Expansions</a>, in Sequences and their Applications, C. Ding, T. Helleseth, and H. Niederreiter, eds., Proceedings of SETA'98 (Singapore, 1998), 308-317, 1999. DOI: 10.1007/978-1-4471-0551-0_23
%F A039972 a(n) = A007317(n) mod 3. - _Christian G. Bower_, Jun 12 2005
%o A039972 (PARI)
%o A039972 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A039972 A039972_as_a_vector(size)= { my(A=vector(size)); for(j=1, size, A[j]=1+sum(k=1, j-1, A[k]*A[j-k])); apply(n->(n%3),A); }; \\ After _Michael Somos_' May 23 2005 code for A007317 and _Christian G. Bower_'s formula for A039972.
%o A039972 write_to_bfile(1,A039972_as_a_vector(6561),"b039972_upto6561.txt"); \\ _Antti Karttunen_, Aug 15 2017
%Y A039972 Cf. A006996, A007317, A010872, A039969.
%K A039972 nonn
%O A039972 1,2
%A A039972 _N. J. A. Sloane_
%E A039972 More terms from _Christian G. Bower_, Jun 12 2005
%E A039972 Formula added to the name by _Antti Karttunen_, Aug 15 2017