|
|
A031740
|
|
Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 62.
|
|
1
|
|
|
962, 3846, 8652, 15380, 24030, 34602, 47096, 61512, 77850, 96110, 116292, 138396, 162422, 188370, 216240, 246032, 277746, 311382, 346940, 384420, 423822, 465146, 508392, 553560, 600650, 649662, 700596, 753452, 808230, 864930, 923552, 984096
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Conjecture: a(n) = n*(961*n+1). a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). G.f.: 2*x*(481+480*x)/(1-x)^3. - Colin Barker, Sep 30 2012
Conjecture is false. m*(961*m+1) for m >= 1 is a subsequence (see comment in A031712) and 3940288 is a term not of the form m*(961*m+1). - Chai Wah Wu, Jun 19 2016
|
|
MATHEMATICA
|
Select[Range[10^6], !IntegerQ[Sqrt[#]]&&Min[ContinuedFraction[Sqrt[#]][[2]]] == 62 &] (* Vincenzo Librandi, Jun 20 2016 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|