A140397 a(n) = floor(3*phi*n) - 3*floor(phi*n) where phi = (1+sqrt(5))/2.

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Offset: 1

Author

Fred Lunnon, Jun 20 2008

Keywords

• nonn

Crossrefs

Cf. A140398, A140399, A140400, A140401, A005652, A005653, A078588.

Programs

Mathematica

a[n_]:=Floor[3GoldenRatio*n]-3Floor[GoldenRatio*n];Array[a,99] (* James C. McMahon, Jul 08 2025 *)

PARI

a(n) = my(fhi=(1+sqrt(5))/2); floor(3*fhi*n) - 3*floor(fhi*n); \\ Michel Marcus, Aug 26 2013

Formula

a(n) = floor(n*s^2)-floor(s*floor(n*s)), where s=1+phi.