A262059 Least integer k such that k^(1/3)/log(k) exceeds n.

2, 4913, 29410, 96854, 236916, 484596, 879483, 1465239, 2289183, 3401984, 4857388, 6712006, 9025131, 11858570, 15276512, 19345406, 24133846, 29712478, 36153913, 43532644, 51924974, 61408954, 72064316, 83972419, 97216198, 111880113, 128050105, 145813554, 165259239, 186477301, 209559205

Offset

1,1

Links

Table of n, a(n) for n=1..31.

Maple

A262059val := proc(k)
    Digits := 100 ;
    evalf(root[3](k)/log(k)) ;
end proc:
A262059lims := proc(n, lowk, highk)
    local vallow, valhigh, midk, valmid ;
    vallow := A262059val(lowk) ;
    valhigh := A262059val(highk) ;
    if valhigh > n and vallow <= n and highk= lowk+1 then
        return highk;
    else
        midk := floor((lowk+highk)/2) ;
        valmid := A262059val(midk) ;
        if valmid < n then
            return procname(n, midk, highk) ;
        else
            return procname(n, lowk, midk) ;
        end if;
    end if;
end proc:
A262059 := proc(n)
    local lowk, highk, p ;
    if n = 1 then
        return 2;
    end if;
    for p from 0 do
        lowk := 10^p ;
        highk := 10^(p+1) ;
        if A262059val(highk) >=n then
            return A262059lims(n, min(2, lowk), highk) ;
        end if;
    end do:
end proc: # R. J. Mathar, Oct 22 2015

Mathematica

f[n_] := f[n] = Block[{k = f[n - 1]}, While[n > k^(1/3)/Log[k], k++]; k]; f[1] = 2; Array[f, 40]

Prog

(PARI) a(n) = {my(k = 2); while(sqrtn(k, 3)/log(k) <= n, k++); k; } \\ Michel Marcus, Sep 10 2015

Crossrefs

Cf. A088346, A262058, A262060.

Sequence in context: A195002 A203756 A232712 * A153737 A078933 A064029

Adjacent sequences: A262056 A262057 A262058 * A262060 A262061 A262062

Keyword

nonn

Author

Robert G. Wilson v, Sep 09 2015

Status

approved