A262060 -id:A262060 - cp's OEIS frontend

A262058 Least integer k>1 such that sqrt(k)/log(k) exceeds n.

2, 2, 289, 681, 1280, 2109, 3190, 4538, 6170, 8100, 10339, 12901, 15795, 19032, 22620, 26570, 30888, 35583, 40662, 46133, 52003, 58277, 64962, 72065, 79590, 87544, 95932, 104759, 114030, 123750, 133924, 144557, 155652, 167215, 179250, 191760

Offset: 1

Robert G. Wilson v, Sep 09 2015

nonn

Danny Rorabaugh, Table of n, a(n) for n = 1..10000

Cf. A088346, A262059, A262060.

A262058 := proc(n)
    Digits := 30 ;
    for k from 2 do
        if evalf(sqrt(k) > n*log(k)) then
            return k;
        end if;
    end do:
end proc: # R. J. Mathar, Oct 22 2015

f[n_] := f[n] = Block[{k = f[n - 1]}, While[n > Sqrt[k]/Log[k], k++]; k]; f[1] = 2; Array[f, 50]

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

def A262058(n,d=50):
    (low,high) = (1,2)
    while N(sqrt(high),digits=d) <= N(n*log(high),digits=d):
        high *= 2
    while low+1Danny Rorabaugh, Sep 26 2015

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

Original entry on oeis.org

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

Robert G. Wilson v, Sep 09 2015

nonn

Cf. A088346, A262058, A262060.

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

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

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

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A262058 Least integer k>1 such that sqrt(k)/log(k) exceeds n.

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