|
|
A107356
|
|
Period of continued fraction for (1 + square root of n-th squarefree integer)/2.
|
|
1
|
|
|
2, 2, 1, 4, 4, 2, 2, 1, 4, 2, 3, 6, 2, 6, 4, 2, 1, 2, 8, 4, 4, 2, 3, 6, 6, 5, 4, 10, 8, 4, 2, 1, 4, 6, 6, 6, 3, 4, 3, 6, 10, 4, 6, 8, 9, 6, 2, 4, 4, 2, 2, 1, 6, 2, 7, 8, 2, 12, 4, 9, 3, 6, 12, 6, 18, 6, 7, 4, 6, 7, 6, 6, 14, 4, 2, 2, 12, 10, 6, 6, 4, 10, 7, 4, 18, 4, 4, 2, 3, 6, 5, 20, 14, 8, 5, 12, 6, 10
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
a(7) = 2 because 11 is the 7th smallest squarefree integer and (1 + sqrt 11)/2 = [2,6,3,6,3,6,3,... ] thus has an eventual period of 2. We omit 1 from the list of squarefree integers.
|
|
MATHEMATICA
|
(* first do *) Needs["NumberTheory`NumberTheoryFunctions`"] (* then *) s = Drop[ Select[ Range[162], SquareFreeQ[ # ] &], 1]; Length[ ContinuedFraction[ # ][[2]]] & /@ ((1 + Sqrt[s])/2) (* Robert G. Wilson v, May 27 2005 *)
Length[ContinuedFraction[(Sqrt[#]+1)/2][[2]]]&/@Select[Range[ 2, 200], SquareFreeQ] (* Harvey P. Dale, Aug 16 2021 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|