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A214051 Least m>0 such that (1+r)^m >= n!, where r = (1+sqrt(5))/2, the golden ratio. 2
1, 1, 2, 4, 5, 7, 9, 12, 14, 16, 19, 21, 24, 27, 29, 32, 35, 38, 41, 44, 48, 51, 54, 57, 61, 64, 68, 71, 75, 78, 82, 85, 89, 93, 96, 100, 104, 107, 111, 115, 119, 123, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

MAPLE

A214051 := proc(n)

    local r, m;

    r := (1+sqrt(5))/2 ;

    for m from 1 do

        if floor((1+r)^m) >= n! then

            return m ;

        end if;

    end do:

end proc: # R. J. Mathar, Jul 23 2012

MATHEMATICA

r=GoldenRatio;

Table[m=1; While[n!>(1+r)^m, m++]; m, {n, 1, 100}]

CROSSREFS

Cf. A214050.

Sequence in context: A053039 A286753 A325543 * A027861 A219648 A062428

Adjacent sequences:  A214048 A214049 A214050 * A214052 A214053 A214054

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jul 18 2012

STATUS

approved

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Last modified February 26 11:49 EST 2020. Contains 332279 sequences. (Running on oeis4.)