A377932 a(n) is the denominator of the third convergent of the continued fraction of n^(1/n).

5, 7, 5, 3, 3, 25, 7, 4, 4, 37, 9, 5, 5, 91, 16, 6, 6, 6, 31, 13, 7, 7, 106, 22, 15, 8, 8, 65, 25, 9, 9, 9, 55, 19, 10, 10, 10, 61, 21, 11, 11, 11, 78, 34, 12, 12, 12, 121, 37, 25, 13, 13, 300, 53, 27, 14, 14, 14, 85, 29, 15, 15, 15, 196, 46, 31, 16, 16, 16

Offset

2,1

Links

Table of n, a(n) for n=2..70.

Example

7/5, 10/7, 7/5, 4/3, 4/3, 33/25, 9/7, 5/4, 5/4, 46/37, 11/9, 6/5, 6/5, 109/91, ...

Maple

c:= n-> (l-> l[1]+1/(l[2]+1/l[3]))(numtheory[cfrac](n^(1/n), 'quotients')):
a:= n-> denom(c(n)):
seq(a(n), n=2..70);  # Alois P. Heinz, Nov 11 2024

Prog

(PARI) \\ uses function cofrnthr from A377931
a377932(n) = denominator(cofrnthr(n, 3))

Crossrefs

A377931 are the corresponding numerators.

Cf. A090663.

Sequence in context: A178668 A198744 A201944 * A165242 A104542 A161376

Adjacent sequences: A377927 A377930 A377931 * A377935 A377936 A377937

Keyword

nonn,frac,new

Author

Hugo Pfoertner, Nov 11 2024

Status

approved