A237274 a(n) = A236283(n) mod 9.

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, 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, 1, 5, 4, 1

Offset: 0

Author

Paul Curtz, Feb 05 2014

Keywords

• nonn

Comments

(Conjecture) This has period 18: repeat 2, 1, 4, 5, 1, 4, 2, 7, 7, 5, 7, 7, 2, 4, 1, 5, 4, 1.

The first 19 terms and the following 17 are palindromes.

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.

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.

A236283(-n) = A236283(n).

A236283(n) difference table:

2, 1, 4, 5, 10, 13, 20, 25, 34, 41,...

-1, 3, 1, 5, 3, 7, 5, 9, 7, 11,... = A097062(n+1)

4, -2, 4, -2, 4, -2, 4, -2, 4, -2,...

-6, 6, -6, 6, -6, 6, -6, 6, -6, 6,... .

A097062(n+1) mod 9 = (a(n+1) -a(n)) mod 9 =

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.

Ordered b(n)=

period 18: repeat 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8.

Formula

a(n) = A236283(n) mod 9.