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a(n) = floor(n^phi) where phi is the golden ratio.
3

%I #25 Oct 20 2024 17:57:25

%S 0,1,3,5,9,13,18,23,28,34,41,48,55,63,71,79,88,97,107,117,127,137,148,

%T 159,171,182,194,207,219,232,245,258,272,286,300,315,329,344,359,375,

%U 391,406,423,439,456,473,490,507,525,542,561,579,597,616,635,654,673

%N a(n) = floor(n^phi) where phi is the golden ratio.

%H Georg Fischer, <a href="/A152737/b152737.txt">Table of n, a(n) for n = 0..9999</a> [first 1615 terms from Paolo P. Lava]

%t a[n_]:=Floor[n^GoldenRatio];

%o (PARI) a(n)=floor(n^((1+sqrt(5))/2)) \\ _Charles R Greathouse IV_, Jul 29 2011

%o (Magma) phi:=(1+Sqrt(5))/2; [Floor(n^phi): n in [0..50]]; // _G. C. Greubel_, Sep 01 2018

%Y Cf. A001622, A014217.

%K nonn,easy

%O 0,3

%A _Vladimir Joseph Stephan Orlovsky_, Dec 12 2008

%E Offset changed to 0 by _Georg Fischer_, Oct 19 2024