A020959 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..500

C. Kimberling, Problem 10520, Amer. Math. Mon. 103 (1996) p. 347.

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 *)

PROG

(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

CROSSREFS

Cf. A001622.

Sequence in context: A263085 A206334 A184741 * A175312 A057640 A182136

Adjacent sequences: A020956 A020957 A020958 * A020960 A020961 A020962

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved