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%I #12 Aug 05 2014 01:02:20
%S 2,1,4,5,1,4,2,7,7,5,7,7,2,4,1,5,4,1,2,1,4,5,1,4,2,7,7,5,7,7,2,4,1,5,
%T 4,1,2,1,4,5,1,4,2,7,7,5,7,7,2,4,1,5,4,1,2,1,4,5,1,4,2,7,7,5,7,7,2,4,
%U 1,5,4,1
%N a(n) = A236283(n) mod 9.
%C (Conjecture) This has period 18: repeat 2, 1, 4, 5, 1, 4, 2, 7, 7, 5, 7, 7, 2, 4, 1, 5, 4, 1.
%C The first 19 terms and the following 17 are palindromes.
%C The sorted terms in the conjectured period are 1, 1, 1, 1, 2, 2, 2, 4, 4, 4, 4, 5, 5, 5, 7, 7, 7, 7.
%C Via the extended differences of A236283(n+1) and A236283(n+18) - A236283(n) which is A008600(n+9)=162, 180,... ,it is easy to see that A236283(0)=2.
%C A236283(-n) = A236283(n).
%C A236283(n) difference table:
%C 2, 1, 4, 5, 10, 13, 20, 25, 34, 41,...
%C -1, 3, 1, 5, 3, 7, 5, 9, 7, 11,... = A097062(n+1)
%C 4, -2, 4, -2, 4, -2, 4, -2, 4, -2,...
%C -6, 6, -6, 6, -6, 6, -6, 6, -6, 6,... .
%C A097062(n+1) mod 9 = (a(n+1) -a(n)) mod 9 =
%C period 18: repeat 8, 3, 1, 5, 3, 7, 5, 0, 7, 2, 0, 4, 2, 6, 4, 8, 6, 1 =b(n). b(n) + b(18-n)= 9, 9, 9, 9, 9, 9, 9, 0, 9.
%C Ordered b(n)=
%C period 18: repeat 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8.
%F a(n) = A236283(n) mod 9.
%K nonn
%O 0,1
%A _Paul Curtz_, Feb 05 2014
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