A180592 Digital root of 2n.

0, 2, 4, 6, 8, 1, 3, 5, 7, 9, 2, 4, 6, 8, 1, 3, 5, 7, 9, 2, 4, 6, 8, 1, 3, 5, 7, 9, 2, 4, 6, 8, 1, 3, 5, 7, 9, 2, 4, 6, 8, 1, 3, 5, 7, 9, 2, 4, 6, 8, 1, 3, 5, 7, 9, 2, 4, 6, 8, 1, 3, 5, 7, 9, 2, 4, 6, 8, 1, 3, 5, 7, 9, 2, 4, 6, 8, 1, 3, 5, 7, 9, 2, 4, 6, 8, 1, 3, 5, 7, 9, 2, 4, 6, 8, 1, 3, 5, 7, 9, 2, 4, 6, 8, 1

Offset: 0

Author

Odimar Fabeny, Sep 10 2010

Keywords

• easy
• nonn
• base

Comments

Period 9. - Robert G. Wilson v, Sep 20 2010

Also digital root of A002276(n). - Enrique Pérez Herrero, Nov 05 2022

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A007953, A010888, A180593, A180594, A180595, A180596, A180597, A180598, A180599.

Programs

Mathematica

f[n_] := Mod[2 n - 1, 9] + 1; f[0] = 0; Array[f, 105, 0] (* Robert G. Wilson v, Sep 20 2010 *)

PARI

a(n)=if(n,(2*n-1)%9+1,0) \\ Charles R Greathouse IV, Aug 25 2014

Formula

From R. J. Mathar, Nov 02 2010: (Start)

a(n) = A010888(2*n).

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

G.f.: -x*(2 + 4*x + 6*x^2 + 8*x^3 + x^4 + 3*x^5 + 5*x^6 + 7*x^7 + 9*x^8) / ( (x-1)*(1 + x + x^2)*(x^6 + x^3 + 1) ). (End)

Extensions

More terms from Robert G. Wilson v, Sep 20 2010

Keyword:base and formulas from R. J. Mathar, Nov 02 2010