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A190142
Decimal expansion of limit sqrt(2’*sqrt(3’*sqrt(4’*sqrt(5’*sqrt(6’*...))))), where n’ is the arithmetic derivative of n.
0
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
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
KEYWORD
nonn,cons
AUTHOR
Paolo P. Lava, May 05 2011
STATUS
approved