OFFSET
1,3
COMMENTS
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
FORMULA
a(n) ~ 3^(-1/3) * n. - Vaclav Kotesovec, Oct 09 2014
EXAMPLE
Let s(n) = sum{1/h^4, h = 1..n}. Approximations are shown here:
n ... zeta(4) - s(n) ... 1/n^3
1 ... 0.0823232 .... 1
2 ... 0.0198232 .... 0.125
3 ... 0.0074775 .... 0.037
4 ... 0.0035713 .... 0.015
5 ... 0.0019713 .... 0.008
6 ... 0.0011997 .... 0.005
a(6) = 4 because zeta(4) - s(4) < 1/216 < zeta(4) - s(3).
MATHEMATICA
$MaxExtraPrecision = Infinity; z = 400; p[k_] := p[k] = Sum[1/h^4, {h, 1, k}];
N[Table[Zeta[4] - p[n], {n, 1, z/10}]]
f[n_] := f[n] = Select[Range[z], Zeta[4] - p[#] < 1/n^3 &, 1];
u = Flatten[Table[f[n], {n, 1, z}]] (* A248227 *)
Flatten[Position[Differences[u], 0]] (* A248228 *)
Flatten[Position[Differences[u], 1]] (* A248229 *)
f = Table[Floor[1/(Zeta[4] - p[n])], {n, 1, z}] (* A248230 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 05 2014
STATUS
approved