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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
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, ...].
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
KEYWORD
nonn,cons
AUTHOR
Paolo P. Lava, Apr 15 2019
STATUS
approved