A361089 a(n) = smallest integer x such that Sum_{k = 2..x} 1/(k*log(log(k))) > n.
3, 5, 8, 21, 76, 389, 2679, 23969, 269777, 3717613, 61326301, 1188642478, 26651213526, 682263659097, 19720607003199, 637490095320530, 22857266906194526, 902495758030572213, 38993221443197045348, 1833273720522384358862
Offset: 2
Keywords
Examples
a(2) = 3 because Sum_{k=2..3} 1/(k*log(log(k))) = 2.18008755... > 2 and Sum_{k=2..2} 1/(k*log(log(k))) = -1.364208386450... < 2.
a(7) = 389 because Sum_{k=2..389} 1/(k*log(log(k))) = 7.000345... > 7 and Sum_{k=2..388} 1/(k*log(log(k))) = 6.99890560988... < 7.
Links
- Pascal Sebah, Table of n, a(n) for n = 2..35
Crossrefs
Programs
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Mathematica
(*slow procedure*) lim = 2; sum = 0; aa = {}; Do[sum = sum + N[1/(k Log[Log[k]]), 100]; If[sum >= lim, AppendTo[aa, k]; Print[{lim, sum, k}]; lim = lim + 1], {k, 2, 269777}];aa (*quick procedure *) aa = {3}; cons = 2.79776470352080492766050456553352884330850083202326989577856315; Do[ww = w /. NSolve[LogIntegral[Log[w]] + cons == n, w]; AppendTo[aa, Round[ww][[1]]], {n, 3, 21}]; aa
Formula
For n >= 3, a(n) = round(w) where w is the solution of the equation li(log(w)) + 2.7977647035208... = n.
Comments