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A073636
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Period 3: repeat [1, 8, 9] ; Digital root of A000578(n) = n^3 for n >= 1.
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5
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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
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: x*(9*x^2+8*x+1)/(1-x^3). - Ant King, Apr 30 2013
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)
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MAPLE
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MATHEMATICA
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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 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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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
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STATUS
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approved
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