A146330 Numbers k such that continued fraction of (1 + sqrt(k))/2 has period 5.

41, 149, 157, 181, 269, 397, 425, 493, 565, 697, 761, 941, 1013, 1037, 1325, 1565, 1781, 1825, 2081, 2153, 2165, 2173, 2465, 2477, 2693, 2725, 3181, 3221, 3533, 3869, 4253, 4409, 5165, 5213, 5273, 5297, 5741, 5837, 6485, 6757, 6949, 7045, 7325, 7465, 8021, 8069

Offset: 1

Author

Artur Jasinski, Oct 30 2008

Keywords

• nonn

Comments

For primes in this sequence see A146350.

Examples

			a(1) = 41 because continued fraction of (1+sqrt(41))/2 = 3, 1, 2, 2, 1, 5, 1, 2, 2, 1, 5, 1, 2, 2, 1, 5, 1, 2, ... has period (1,2,2,1,5) length 5.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000290, A078370, A146326-A146345, A146348-A146360.

Programs

Maple

isA146330 := proc(n) RETURN(A146326(n) = 5) ; end:
for n from 2 to 2000 do if isA146330(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Sep 06 2009

Mathematica

Select[Range[10^4], !IntegerQ @ Sqrt[#] && Length[ContinuedFraction[(1 + Sqrt[#])/2][[2]]] == 5 &]  (* Amiram Eldar, Mar 31 2020 *)

Extensions

259 and 1026 removed by R. J. Mathar, Sep 06 2009

More terms from Amiram Eldar, Mar 31 2020