OFFSET
1,2
COMMENTS
For the first 191 terms, a(n) has the form p*2^i, where p is prime and i >= 0. - T. D. Noe, Mar 07 2011
Looking at just the periodic part of sqrt(k), it is the same sequence without the term a(1). - Robert G. Wilson v, Mar 22 2011
Conjecture: a(n) is of the form p, 2*p or 4*p, where p is prime. For the first 528 terms, a(n) is of the form 4*p only for n = 10, 11, 12, 14, 81 and 277. - Chai Wah Wu, Oct 04 2019
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..528 (terms 1..191 from Robert G. Wilson v)
EXAMPLE
ContinuedFraction(sqrt(2),x) => 1,2,2,2,...: two distinct terms (1,2);
sqrt(7) => 2,1,1,1,4,1,1,1,...: three distinct terms (1,2,4);
sqrt(14) => four distinct terms (1,2,3,6);
sqrt(19) => five distinct terms (1,2,3,4,8).
MATHEMATICA
f[n_] := Length@ Union@ Flatten@ ContinuedFraction@ Sqrt@ n; t = Table[ 0, {100}]; Do[a = f@ k; If[ a <= 100 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]], {k, 10^5}]; t
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Mar 05 2011
STATUS
approved