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A135455
Numbers n such that n*phi is within 0.1 of an integer, where phi is the golden ratio.
1
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
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
KEYWORD
easy,nonn
AUTHOR
Ben Paul Thurston, Dec 15 2007
EXTENSIONS
Edited and extended by Stefan Steinerberger, Feb 20 2008
STATUS
approved