%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