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A307565 Decimal representation of continued fraction 1', 2', 3', 4', ..., where n' is the arithmetic derivative of n. 0
1, 8, 2, 9, 2, 2, 2, 5, 9, 1, 7, 8, 8, 0, 4, 4, 3, 6, 2, 8, 0, 2, 8, 7, 0, 2, 2, 2, 6, 6, 6, 1, 5, 1, 4, 9, 2, 1, 7, 5, 8, 7, 5, 7, 7, 1, 4, 8, 3, 7, 3, 8, 6, 5, 3, 4, 2, 8, 3, 2, 5, 4, 6, 2, 0, 6, 9, 4, 8, 8, 7, 1, 0, 4, 3, 1, 7, 7, 4, 9, 3, 5, 7, 8, 0, 2, 4, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A rational approximation (correct up to the 8th decimal digit) is 41977/22948.

Continued fraction: [0, 1, 1, 4, 1, 5, 1, 12, 6, 7, 1, 16, 1, 9, 8, ...].

LINKS

Table of n, a(n) for n=1..88.

EXAMPLE

1.8292225917880443628028702226661514921758757714837386534...

MAPLE

with(numtheory); P:=proc(q) local a, n, p; a:=0;

for n from q by -1 to 1 do

a:=1/(a+n*add(op(2, p)/op(1, p), p=ifactors(n)[2]));

od; print(evalf(a, 200)); end: P(10^3);

CROSSREFS

Cf. A003415.

Sequence in context: A296301 A019865 A198993 * A119523 A181164 A154212

Adjacent sequences:  A307562 A307563 A307564 * A307566 A307567 A307568

KEYWORD

nonn,cons

AUTHOR

Paolo P. Lava, Apr 15 2019

STATUS

approved

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Last modified July 15 00:36 EDT 2020. Contains 335762 sequences. (Running on oeis4.)