A135455 Numbers n such that n*phi is within 0.1 of an integer, where phi is the golden ratio.

5, 8, 13, 21, 26, 29, 34, 42, 47, 50, 55, 60, 63, 68, 76, 81, 84, 89, 94, 97, 102, 110, 115, 118, 123, 131, 136, 139, 144, 149, 152, 157, 165, 170, 173, 178, 186, 191, 199, 204, 207, 212, 220, 225, 228, 233, 238, 241, 246, 254, 259, 262, 267, 275, 280, 283, 288

Offset

1,1

Comments

By using the formula of Binet one can easily show that all Fibonacci numbers greater than 3 are in the sequence. Furthermore the sequence a(n)/n converges to 1/5.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) ~ 5n by the equidistribution theorem. - Charles R Greathouse IV, Oct 14 2016

Example

47 is in the sequence because 1.6180339887*47 = 76.047 which is within .1 of an integer.

Mathematica

Select[Range[300], Abs[ #*(1 + Sqrt[5])/2 - Round[ #*(1 + Sqrt[5])/2]] < 0.1 &] (* or *) grw1Q[n_]:=Module[{c=n*GoldenRatio}, Abs[c-Round[c]]<=.1]; Select[Range[ 300], grw1Q] (* Harvey P. Dale, Mar 20 2015 *)

Prog

(PARI) is(n)=my(phi=(sqrt(5)+1)/2); frac(n/phi + .1) < .2 \\ Charles R Greathouse IV, Oct 14 2016

Crossrefs

Cf. A000045.

Sequence in context: A314462 A314463 A314464 * A020712 A369222 A369220

Adjacent sequences: A135452 A135453 A135454 * A135456 A135457 A135458

Keyword

easy,nonn

Author

Ben Paul Thurston, Dec 15 2007

Extensions

Edited and extended by Stefan Steinerberger, Feb 20 2008

Status

approved