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A020959
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a(n) = Sum_{k>=1} floor(n*phi^(1-k)).
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4
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1, 3, 5, 7, 10, 12, 15, 17, 20, 22, 24, 27, 30, 33, 35, 37, 40, 43, 45, 47, 50, 53, 56, 58, 60, 63, 65, 68, 70, 74, 76, 78, 80, 84, 87, 90, 92, 94, 97, 99, 101, 104, 107, 109, 112, 114, 118, 121, 123, 125, 128, 130, 132, 135, 138, 142, 144, 146, 149, 152, 154
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OFFSET
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1,2
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LINKS
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C. Kimberling, Problem 10520, Amer. Math. Mon. 103 (1996) p. 347.
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MAPLE
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a:=n->add(floor(n*((1+sqrt(5))/2)^(1-k)), k=1..n): seq(a(n), n=1..61); # Muniru A Asiru, Oct 09 2018
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MATHEMATICA
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a[n_] := Sum[ Floor[ n*GoldenRatio^(1 - k)], {k, 1, Ceiling[1 - Log[1/n] / ArcCsch[2]]}]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Sep 18 2013 *)
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PROG
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(PARI) a(n) = my(res = 0, s, gratio = (1 + sqrt(5)) / 2); for(k = 1, oo, s = floor(n*gratio^(1-k)); if(s==0, return(res), res+=s)) \\ David A. Corneth, Oct 09 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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