A214051 Least m>0 such that (1+r)^m >= n!, where r = (1+sqrt(5))/2, the golden ratio.

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

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