A180593 Digital root of 3n.

0, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, 6

Offset: 0

Author

Odimar Fabeny, Sep 10 2010

Keywords

• nonn
• base
• easy

Comments

Decimal expansion of 41/1110. - Enrique Pérez Herrero, Nov 13 2021

Links

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

Crossrefs

Cf. A008585 (3*n), A010888 (digital root), A002277.

Cf. A180592, A180594, A180595, A180596, A180597, A180598, A180599.

Programs

Mathematica

digitalRoot[n_Integer?Positive] := FixedPoint[Plus@@IntegerDigits[#]&,n]; Table[If[n==0,0,digitalRoot[3*n]], {n,0,200}] (* Vladimir Joseph Stephan Orlovsky, May 02 2011 *)
LinearRecurrence[{0,0,1},{0,3,6,9},120] (* Harvey P. Dale, Sep 03 2020 *)

Formula

a(n+1) = 3*A010882(n). - Reinhard Zumkeller, Oct 25 2010

G.f.: (-3*(1 + 2*x + 3*x^2))/(-1 + x^3) for n>0. - Alexander R. Povolotsky, Jun 13 2012

a(n) = A010888(A002277(n)). - Enrique Pérez Herrero, Nov 24 2022

a(n) = A010888(A008585(n)). - Michel Marcus, Nov 24 2022

Extensions

Edited by N. J. A. Sloane, Sep 23 2010