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A248234 a(n) = floor(1/(zeta(5) - Sum_{h=1..n} 1/h^5)). 4
27, 176, 639, 1706, 3759, 7279, 12842, 21119, 32879, 48986, 70399, 98175, 133466, 177519, 231679, 297386, 376175, 469679, 579626, 707839, 856239, 1026842, 1221759, 1443199, 1693466, 1974959, 2290175, 2641706, 3032239, 3464559, 3941546, 4466175, 5041519 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence provides insight into the manner of convergence of Sum_{h=1..n} 1/h^5.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..2000

Soumyadip Sahu, On Certain Reciprocal Sums, arXiv:1807.05454 [math.NT], 2018.

FORMULA

Empirically, a(n) = 4*a(n-1) - 6*a(n-2) + 5*a(n-3) - 5*a(n-4) + 6*a(n-5) - 4*a(n-6) + a(n-7), for n >= 10.

Conjecture (for n >= 3): (12*n*(1+n)*(4+3*n+3*n^2) - 8 - cos(2*n*Pi/3) + sqrt(3)*sin(2*n*Pi/3))/9. - Vaclav Kotesovec, Oct 09 2014

MATHEMATICA

z = 400; p[k_] := p[k] = Sum[1/h^5, {h, 1, k}]; N[Table[Zeta[5] - p[n], {n, 1, z/10}]]

f[n_] := f[n] = Select[Range[z], Zeta[5] - p[#] < 1/n^4 &, 1]

u = Flatten[Table[f[n], {n, 1, z}]]   (* A248231 *)

Flatten[Position[Differences[u], 0]]  (* A248232 *)

Flatten[Position[Differences[u], 1]]  (* A248233 *)

Table[Floor[1/(Zeta[5] - p[n])], {n, 1, z}]  (* A248234 *)

CROSSREFS

Cf. A248231, A248232, A248233, A248227, A013663.

Sequence in context: A174617 A055339 A269054 * A083560 A125337 A126495

Adjacent sequences:  A248231 A248232 A248233 * A248235 A248236 A248237

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 05 2014

STATUS

approved

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Last modified August 20 08:27 EDT 2019. Contains 326143 sequences. (Running on oeis4.)