login
Numbers n not of form k(k+2) that have a single '1' in the periodic part of the continued fraction of sqrt(n).
2

%I #9 Mar 14 2015 16:46:53

%S 175,176,208,551,799,1035,1247,1403,1872,2856,2967,3395,3496,3503,

%T 3531,3731,3864,3999,4136,4387,4416,4512,4543,5343,5368,5499,5520,

%U 6099,6160,6608,6751,7791,8855,9048,10439,10664,10904,11323,11935,12208,13299

%N Numbers n not of form k(k+2) that have a single '1' in the periodic part of the continued fraction of sqrt(n).

%C Members of A013648 not in A005563.

%C No prime numbers? - Zak Seidov, Feb 28 2012

%H Zak Seidov, <a href="/A102538/b102538.txt">Table of n, a(n) for n = 1..1000</a>

%t fQ[n_] := Block[{k = Floor[Sqrt[n]]}, If[ k(k + 2) != n && !IntegerQ[ Sqrt[n]], cof = Sort[ ContinuedFraction[ Sqrt[n]] [[2]]]; If[ cof[[1]] == 1 && cof[[2]] != 1, True]]]; Select[ Range[ 13986], fQ[ # ] &] (* _Robert G. Wilson v_, Jan 25 2005 *)

%K nonn

%O 1,1

%A _Ralf Stephan_, Jan 14 2005

%E More terms from _Robert G. Wilson v_, Jan 25 2005