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A073636
Period 3: repeat [1, 8, 9] ; Digital root of A000578(n) = n^3 for n >= 1.
5
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
1,2
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
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)
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
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