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 A105669 A "fractal" transform of the Fibonacci numbers F(n)=A000045(n): a(1)=1, then for n>1 if F(n)
 1, 2, 2, 4, 7, 7, 6, 6, 12, 11, 11, 9, 20, 20, 19, 19, 17, 14, 14, 15, 15, 33, 32, 32, 30, 27, 27, 28, 28, 22, 23, 23, 25, 54, 54, 53, 53, 51, 48, 48, 49, 49, 43, 44, 44, 46, 35, 35, 36, 36, 38, 41, 41, 40, 40, 88, 87, 87, 85, 82, 82, 83, 83, 77, 78, 78, 80, 69, 69, 70, 70, 72 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Let b denote the sequence of n such that a(n)=a(n+1), then b(n)=floor(tau^2*n) where tau=(1+sqrt(5))/2 Missing numbers are the nearest integer to tau^2*n, n>=0 (cf. A004937) #{k>0:a(k)=k}=infinity This kind of "fractal" transform can be applied to any increasing monotonic sequence giving true fractal properties for sequences = (m^n)_{n>0} with m integer >=2, specially when m is odd (cf. A093347, A093348 ) LINKS FORMULA n>0 a(F(2n))=F(2n+1)-F(n+1)^2+F(n)F(n-1) n>1 a(F(2n-1))=F(2n)-1 1/tau < a(n)/n < tau. EXAMPLE for 5=F(5)

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Last modified October 14 01:36 EDT 2019. Contains 327994 sequences. (Running on oeis4.)