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A073636 Period 3: repeat [1, 8, 9] ; Digital root of A000578(n) = n^3 for n >= 1. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

Table of n, a(n) for n=1..87.

Eric Weisstein's World of Mathematics, Digital Root.

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

FORMULA

a(n) = (1/3)*{14*[(n-1) mod 3]+5*[n mod 3]-[(n+1) mod 3]}. - Paolo P. Lava, Jun 08 2007

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)

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 *)

PROG

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

CROSSREFS

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

Sequence in context: A155553 A302765 A053463 * A113521 A297537 A030167

Adjacent sequences:  A073633 A073634 A073635 * A073637 A073638 A073639

KEYWORD

nonn,base,easy

AUTHOR

Zak Seidov, Sep 01 2002

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

STATUS

approved

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Last modified October 22 18:31 EDT 2019. Contains 328319 sequences. (Running on oeis4.)