A307565 Decimal representation of continued fraction 1', 2', 3', 4', ..., where n' is the arithmetic derivative of n.

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

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