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%I #23 Oct 11 2018 12:02:51
%S 1,3,5,7,10,12,15,17,20,22,24,27,30,33,35,37,40,43,45,47,50,53,56,58,
%T 60,63,65,68,70,74,76,78,80,84,87,90,92,94,97,99,101,104,107,109,112,
%U 114,118,121,123,125,128,130,132,135,138,142,144,146,149,152,154
%N a(n) = Sum_{k>=1} floor(n*phi^(1-k)).
%H Muniru A Asiru, <a href="/A020959/b020959.txt">Table of n, a(n) for n = 1..500</a>
%H C. Kimberling, <a href="http://www.jstor.org/stable/2975195">Problem 10520</a>, Amer. Math. Mon. 103 (1996) p. 347.
%p 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
%t 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 *)
%o (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
%Y Cf. A001622.
%K nonn
%O 1,2
%A _Clark Kimberling_
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