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

0,1

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.

Links

Table of n, a(n) for n=0..71.

Formula

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

Crossrefs

Sequence in context: A349994 A194363 A161135 * A038730 A188106 A050166

Adjacent sequences: A237271 A237272 A237273 * A237275 A237276 A237277

Keyword

nonn

Author

Paul Curtz, Feb 05 2014

Status

approved