A073636 Period 3: repeat [1, 8, 9] ; Digital root of A000578(n) = n^3 for n >= 1.

1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9

Offset: 1

Author

Zak Seidov, Sep 01 2002

Keywords

• nonn
• base
• easy

Comments

a(n) is the decimal expansion of 70/37. [Enrique Pérez Herrero, Jul 28 2009]; corrected by David A. Corneth, Jun 30 2016

Links

• Eric Weisstein's World of Mathematics, Digital Root.
• Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Crossrefs

Cf. A000578, A004164, A010888, A021596. Digital roots of squares are in A056992.

Programs

Magma

&cat [[1, 8, 9]^^30]; // Wesley Ivan Hurt, Jun 30 2016

Maple

seq(op([1, 8, 9]), n=1..50); # Wesley Ivan Hurt, Jun 30 2016

Mathematica

n=3; su[x_] := Sum[IntegerDigits[x][[i]], {i, Length[IntegerDigits[x]]}]; Table[su[su[su[su[x^n]]]], {x, 100}]
NestWhile[Total[IntegerDigits[#]] &, #1, # > 9 &] & /@ (Range[87]^3) (* Jayanta Basu, Jul 03 2013 *)

Formula

G.f.: x*(9*x^2+8*x+1)/(1-x^3). - Ant King, Apr 30 2013

From Wesley Ivan Hurt, Jun 30 2016: (Start)

a(n) = a(n-3) for n>3.

a(n) = 6 + 3*cos(2*n*Pi/3) - 7*sin(2*n*Pi/3)/sqrt(3). (End)

Extensions

Decimal expansion fraction corrected by Ant King, Apr 30 2013

Edited: name specified, offset changed from 0 to 1 (according to name), adjusted formula and g.f. for offset 1, digital root link added. - Wolfdieter Lang, Jan 05 2015