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A190143 Decimal expansion of continued fraction 1’+1/(2’+1/(3’+1/(4’+1/(5’…)))), where n’ is the arithmetic derivative of n. 1
5, 4, 6, 6, 8, 0, 3, 2, 4, 4, 6, 6, 4, 2, 3, 3, 7, 1, 4, 6, 2, 1, 7, 2, 7, 2, 4, 7, 0, 9, 5, 0, 0, 2, 7, 2, 2, 6, 3, 0, 2, 5, 6, 8, 9, 8, 5, 2, 7, 9, 2, 1, 6, 6, 1, 4, 5, 4, 3, 4, 9, 8, 1, 2, 6, 4, 9, 0, 4, 2, 0, 4, 8, 4, 0, 8, 5, 9, 4, 9, 0, 0, 9, 7, 3, 2, 6, 7, 0, 6, 5, 1, 6, 0, 3, 7, 3, 0, 3, 0, 4, 0, 6, 8, 2, 1, 6, 0, 7, 7, 4, 4, 8, 4, 2, 9, 0, 5, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Good approximation up to the 9th decimal digit with 22948/41977.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

EXAMPLE

.546680324466423...

MAPLE

with(numtheory);

P:=proc(i)

local a, f, n, p, pfs;

a:=0;

for n from i by -1 to 1 do

  pfs:=ifactors(n)[2];

  f:=n*add(op(2, p)/op(1, p), p=pfs);

  a:=1/(a+f);

od;

print(evalf(1/a, 1000));

end:

P(10000);

MATHEMATICA

digits = 119; d[0] = d[1] = 0; d[n_] := d[n] = n*Total[Apply[#2/#1 &, FactorInteger[n], {1}]]; f[m_] := f[m] = Fold[d[#2] + 1/#1 &, 1, Range[m] // Reverse] // RealDigits[#, 10, digits] & // First; f[digits]; f[m = 2 digits]; While[f[m] != f[m/2], m = 2 m]; f[m] (* Jean-François Alcover, Feb 21 2014 *)

CROSSREFS

Cf. A003415.

Sequence in context: A075194 A138255 A153451 * A089687 A251792 A159894

Adjacent sequences:  A190140 A190141 A190142 * A190144 A190145 A190146

KEYWORD

nonn,cons

AUTHOR

Paolo P. Lava, May 05 2011

STATUS

approved

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Last modified September 15 16:12 EDT 2019. Contains 327078 sequences. (Running on oeis4.)