A020959 a(n) = Sum_{k>=1} floor(n*phi^(1-k)).

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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..500
• C. Kimberling, Problem 10520, Amer. Math. Mon. 103 (1996) p. 347.

Crossrefs

Cf. A001622.

Programs

Maple

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

Mathematica

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 *)

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