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

Author

Robert G. Wilson v, Sep 09 2015

Keywords

• nonn

Crossrefs

Cf. A088346, A262058, A262060.

Programs

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]

PARI

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