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 A130234 Minimal index k of a Fibonacci number such that Fibonacci(k) >= n (the 'upper' Fibonacci Inverse). 23
 0, 1, 3, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Inverse of the Fibonacci sequence (A000045), nearly, since a(Fibonacci(n)) = n except for n = 2 (see A130233 for another version). a(n+1) is equal to the partial sum of the Fibonacci indicator sequence (see A104162). LINKS FORMULA a(n) = ceiling(log_phi((sqrt(5)*n + sqrt(5*n^2-4))/2)) = ceiling(arccosh(sqrt(5)*n/2)/log(phi)) where phi = (1+sqrt(5))/2, the golden ratio, for n > 0. a(n) = A130233(n-1) + 1 for n > 0. G.f.: x/(1-x) * Sum_{k >= 0} x^Fibonacci(k). a(n) = ceiling(log_phi(sqrt(5)*n - 1)) for n > 0, where phi is the golden ratio. - Hieronymus Fischer, Jul 02 2007 a(n) = A108852(n-1). - R. J. Mathar, Jan 31 2015 EXAMPLE a(10) = 7, since Fibonacci(7) = 13 >= 10 but Fibonacci(6) = 8 < 10. MAPLE A130234 := proc(n)     local i;     for i from 0 do         if A000045(i) >= n then             return i;         end if;     end do: end proc: # R. J. Mathar, Jan 31 2015 MATHEMATICA a[n_] := For[i = 0, True, i++, If[Fibonacci[i] >= n, Return[i]]]; a /@ Range[0, 80] (* Jean-François Alcover, Apr 13 2020 *) PROG (PARI) a(n)=my(k); while(fibonacci(k)

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Last modified July 24 06:56 EDT 2021. Contains 346273 sequences. (Running on oeis4.)