A181885 -id:A181885 - cp's OEIS frontend

A172128 a(n) = floor(phi^n/n), where phi = golden ratio = (1+sqrt(5))/2.

1, 1, 1, 1, 2, 2, 4, 5, 8, 12, 18, 26, 40, 60, 90, 137, 210, 320, 492, 756, 1165, 1800, 2786, 4320, 6710, 10440, 16266, 25380, 39650, 62016, 97108, 152213, 238824, 375060, 589521, 927368, 1459960, 2300100, 3626213, 5720653, 9030450, 14263680, 22542396, 35645400

Offset: 1

Clark Kimberling, Nov 20 2010

nonn

G. C. Greubel, Table of n, a(n) for n = 1..4500

Cf. A000045, A001622 (phi), A181885.

[Floor((Lucas(n) + Sqrt(5)*Fibonacci(n))/(2*n)): n in [1..50]]; // G. C. Greubel, Apr 17 2022

Table[Floor[((1 + Sqrt[5])/2)^n/n], {n, 1, 50}]
Table[Floor[GoldenRatio^n/n],{n,50}] (* Harvey P. Dale, Dec 12 2018 *)

[floor(golden_ratio^n/n) for n in (1..50)] # G. C. Greubel, Apr 17 2022

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

A272318 Integer values of Lucas number A000032(n)/n.

Original entry on oeis.org

1, 3, 321, 3572225067, 44308057022098435739157981016569

Offset: 1

Peter M. Chema, Apr 25 2016

nonn

The digital root of this sequence appears to be alternately 3 and 6, aside from the initial term of "1".

A subsequence of A181885. For instance, a(2)=A181885(6), a(3)=A181885(18), a(4)=A181885(54); a(5)=A181885(162); and, a(6)=A181885(486). Also 6, 18, 54, 162 and 486 are consecutive terms of the Pinot sequence A008776. Is this a coincidence?

Andrew Howroyd, Table of n, a(n) for n = 1..9

Cf. A000032, A008776, A016089, A167745, A181885, A167745 and A016089.

LucasL[#]/# & /@ Range@ 1200 /. _Rational -> Nothing (* Version 10.2, or *)
Select[Array[LucasL[#]/# &, {1200}], IntegerQ] (* Michael De Vlieger, Apr 25 2016 *)

a(n) = A000032(A016089(n))/n. - Michel Marcus, Apr 25 2016

cp's OEIS Frontend

A172128 a(n) = floor(phi^n/n), where phi = golden ratio = (1+sqrt(5))/2.

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