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A130234 Minimal index k of a Fibonacci number such that Fib(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(Fib(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

Table of n, a(n) for n=0..80.

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^Fib(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 Fib(7) = 13 >= 10 but Fib(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

PROG

(PARI) a(n)=my(k); while(fibonacci(k)>n, k++); k \\ Charles R Greathouse IV, Feb 03 2014

CROSSREFS

Partial sums: A130236.

Other related sequences: A000045, A130234, A130256, A130260, A104162, A108852, A130256, A130260.

Lucas inverse: A130241 - A130248.

Sequence in context: A266898 A098200 A092405 * A108852 A179413 A119476

Adjacent sequences:  A130231 A130232 A130233 * A130235 A130236 A130237

KEYWORD

nonn,easy

AUTHOR

Hieronymus Fischer, May 17 2007

STATUS

approved

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Last modified December 11 07:47 EST 2019. Contains 329914 sequences. (Running on oeis4.)