A190142 Decimal expansion of limit sqrt(2’*sqrt(3’*sqrt(4’*sqrt(5’*sqrt(6’*...))))), where n’ is the arithmetic derivative of n.

1, 2, 9, 1, 3, 4, 3, 1, 7, 2, 1, 0, 7, 2, 5, 9, 5, 4, 6, 1, 3, 8, 8, 2, 2, 9, 5, 6, 5, 3, 3, 4, 3, 8, 6, 9, 7, 0, 3, 2, 2, 0, 5, 0, 2, 2, 9, 6, 1, 8, 7, 4, 2, 4, 0, 3, 6, 5, 9, 8, 4, 8, 6, 7, 3, 9, 6, 4, 3, 9, 4, 9, 0, 6, 5, 2, 4, 1, 4, 9, 4, 0, 8, 9, 9, 7, 7, 9, 0, 3, 7, 0, 7, 9, 3, 4, 1, 3, 7, 3, 3, 8, 0, 0, 4

Offset

1,2

Links

Table of n, a(n) for n=1..105.

Example

1.29134317210725954613882...

Maple

with(numtheory);
P:=proc(i)
local a, f, n, p, pfs;
a:=1;
for n from i by -1 to 2 do
  pfs:=ifactors(n)[2];
  f:=n*add(op(2, p)/op(1, p), p=pfs) ;
  a:=f*sqrt(a);
od;
print(evalf(sqrt(a), 150));
end:
P(500);

Mathematica

digits = 105; d[0] = d[1] = 0; d[n_] := d[n] = n*Total[Apply[#2/#1 &, FactorInteger[n], {1}]]; f[n_] := f[n] = Fold[Sqrt[d[#2]*#1]&, n, Range[n-1, 2, -1]] // RealDigits[#, 10, digits]& // First; f[digits]; f[n = 2*digits]; While[f[n] != f[n/2], n = 2*n]; f[n] (* Jean-François Alcover, Feb 21 2014 *)

Crossrefs

Cf. A003415, A112302, A171759, A188834, A188835.

Sequence in context: A086773 A176124 A190411 * A173995 A272868 A074950

Adjacent sequences: A190139 A190140 A190141 * A190143 A190144 A190145

Keyword

nonn,cons

Author

Paolo P. Lava, May 05 2011

Status

approved