%I #22 May 01 2021 06:48:21

%S 6,7,8,14,20,23,24,28,32,33,34,42,47,48,52,55,60,62,69,72,75,78,79,80,

%T 95,98,110,119,120,126,133,135,136,138,140,141,142,156,167,168,174,

%U 180,189,194,205,210,213,215,219,220,222,223,224,248,252,254,272,287,288

%N Numbers k such that continued fraction of (1 + sqrt(k))/2 has period 4.

%C For primes in this sequence see A028871 - {2}.

%H Amiram Eldar, <a href="/A146329/b146329.txt">Table of n, a(n) for n = 1..10000</a>

%e a(2) = 7 because continued fraction of (1 + sqrt(7))/2 = 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, ... has period (1,1,4,1) length 4.

%p isA146329 := proc(n) RETURN(A146326(n) = 4) ; end:

%p for n from 2 to 400 do if isA146329(n) then printf("%d,",n) ; fi; od: # _R. J. Mathar_, Sep 06 2009

%t cf4Q[n_]:=Module[{s=(1+Sqrt[n])/2},If[IntegerQ[s],1,Length[ ContinuedFraction[ s][[2]]]]==4]; Select[Range[300],cf4Q] (* _Harvey P. Dale_, Dec 14 2017 *)

%Y Cf. A000290, A078370, A146326-A146345, A028871, A146348-A146360.

%K nonn

%O 1,1

%A _Artur Jasinski_, Oct 30 2008

%E 39, 68, 150, 155, etc. removed by _R. J. Mathar_, Sep 06 2009