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A109918
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n-th digit after decimal point in phi^n, where phi = (1 + sqrt(5))/2.
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0
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6, 1, 6, 1, 6, 1, 8, 6, 7, 2, 4, 4, 4, 5, 7, 1, 8, 0, 3, 2, 7, 4, 1, 5, 2, 4, 9, 8, 2, 9, 1, 7, 8, 6, 3, 3, 3, 5, 1, 1, 3, 8, 9, 1, 6, 7, 4, 5, 6, 4, 6, 8, 3, 6, 0, 7, 1, 9, 8, 3, 2, 5, 6, 4, 8, 3, 6, 4, 8, 9, 4, 2, 9, 1, 1, 9, 6, 1, 4, 5, 3, 0, 5, 1, 7, 8, 5, 0, 7, 0, 2, 8, 9, 1, 7, 1, 4, 1, 7, 9, 3, 2, 4, 0, 9
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OFFSET
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1,1
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COMMENTS
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phi^2-phi=1, so phi^2 and phi have the same digits after the decimal point. Can someone find a number k in which the n-th digit after the decimal point in k^n is constant or follows a pattern?
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LINKS
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MATHEMATICA
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a[n_] := Block[{rd = RealDigits[ GoldenRatio^n, 10, 200]}, rd[[1, rd[[2]] + n]]]; Table[ a[n], {n, 105}] (* Robert G. Wilson v, Jul 19 2005 *)
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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