A256676 Digital roots of centered 11-gonal numbers (A069125).

1, 3, 7, 4, 3, 4, 7, 3, 1, 1, 3, 7, 4, 3, 4, 7, 3, 1, 1, 3, 7, 4, 3, 4, 7, 3, 1, 1, 3, 7, 4, 3, 4, 7, 3, 1, 1, 3, 7, 4, 3, 4, 7, 3, 1, 1, 3, 7, 4, 3, 4, 7, 3, 1, 1, 3, 7, 4, 3, 4, 7, 3, 1, 1, 3, 7, 4, 3, 4, 7, 3, 1, 1, 3, 7, 4, 3, 4, 7, 3, 1, 1, 3, 7, 4, 3

Offset: 1

Author

Colin Barker, Apr 07 2015

Keywords

• nonn
• base
• easy

Comments

The sequence is periodic with period 9.

Examples

			a(3) = 7 because the 3rd centered 11-gonal number is 34, the digital root of which is 7.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 1).

Crossrefs

Cf. A010888, A069125.

Programs

Magma

&cat[[1,3,7,4,3,4,7,3,1]: n in [0..10] ]; // Vincenzo Librandi, Apr 08 2015

Mathematica

PadRight[{}, 100, {1, 3, 7, 4, 3, 4, 7, 3, 1}] (* Vincenzo Librandi, Apr 08 2015 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1},{1, 3, 7, 4, 3, 4, 7, 3, 1},86] (* Ray Chandler, Aug 26 2015 *)

PARI

m=11; vector(200, n, (m*n*(n-1)/2)%9+1)

Formula

a(n) = A010888(A069125(n)).

a(n) = a(n-9).

G.f.: -x*(x^8+3*x^7+7*x^6+4*x^5+3*x^4+4*x^3+7*x^2+3*x+1) / ((x-1)*(x^2+x+1)*(x^6+x^3+1)).