%I #18 Mar 17 2017 22:06:23

%S 1,2,2,2,2,3,4,4,4,4,5,6,7,7,7,8,9,10,10,10,11,12,13,13,13,13,14,15,

%T 15,15,15,16,17,18,18,18,19,20,21,21,21,22,23,24,24,24,24,25,26,26,26,

%U 26,27,28,28,28,28,29,30,31,31,31,32,33,34,34,34,34,35,36,36,36,36,37,38

%N Partial sums of A085002.

%H Antti Karttunen, <a href="/A085003/b085003.txt">Table of n, a(n) for n = 1..10946</a>

%H B. Cloitre, <a href="http://web.archive.org/web/20060326144944/http://membres.lycos.fr/bgourevitch/temporaires/benoit/phifractal.jpg">Graph of A085005(n) for n=1 up to 3874</a> [archive.org link]

%F a(n)=sum(k=1, n, A085002(k)).

%F a(A283766(n)) = n for all n >= 1. - _Antti Karttunen_, Mar 17 2017

%t Accumulate[Table[Floor[GoldenRatio*n]-2*Floor[GoldenRatio*n/2],{n,110}]] (* _Harvey P. Dale_, Dec 11 2012 *)

%o (PARI) sum(k=1,n,(k+sqrtint(5*k^2))%4>1) \\ _Charles R Greathouse IV_, Feb 07 2013

%o (Scheme, with memoization-macro definec)

%o (definec (A085003 n) (if (= 1 n) n (+ (A085002 n) (A085003 (- n 1)))))

%o ;; _Antti Karttunen_, Mar 17 2017

%Y Partial sums of A085002. A left inverse of A283766.

%Y Cf. A083035, A083036, A083037, A083038, A085004, A085005.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Jun 17 2003