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A256007 Numbers k satisfying |k + 1 - 2F| <= 1 for some positive Fibonacci number F. 1
0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 15, 16, 24, 25, 26, 40, 41, 42, 66, 67, 68, 108, 109, 110, 176, 177, 178, 286, 287, 288, 464, 465, 466, 752, 753, 754, 1218, 1219, 1220, 1972, 1973, 1974, 3192, 3193, 3194, 5166, 5167, 5168, 8360, 8361, 8362, 13528, 13529 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For r > 0, define f(n) = floor(n*r) if n is odd and f(n) = floor(n/r) if n is even.  Let S(r,n) be the set {n, f(n), f(f(n)), ...} of iterates of f starting with n.  Conjecture:  if r = (1 + sqrt(5))/2, then S(r,n) is bounded if and only if n is in this sequence.

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..1000

FORMULA

Conjectures from Colin Barker, May 24 2015: (Start)

  a(n) = 2*a(n-3)-a(n-9) for n>12.

  G.f.: -x*(x^11+x^10+x^9+2*x^8+x^7-x^4-2*x^3-3*x^2-2*x-1) / ((x-1)*(x^2+x+1)*(x^6+x^3-1)).

(End)

EXAMPLE

F(1) = F(2) contributes {0,1,2}; F(3) contributes {1,2,3}.

MATHEMATICA

u = Table[Fibonacci[k], {k, 2, 30}]; Union[2 u - 2, 2 u - 1, 2 u]

CROSSREFS

Cf. A000045, A001588, A019274.

Sequence in context: A022773 A049997 A226857 * A324689 A280578 A303878

Adjacent sequences:  A256004 A256005 A256006 * A256008 A256009 A256010

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 07 2015

STATUS

approved

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)