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

1,1

Comments

For primes in this sequence see A146350.

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A254898 A217087 A303910 * A146350 A050954 A337872

Adjacent sequences: A146327 A146328 A146329 * A146331 A146332 A146333

Keyword

nonn

Author

Artur Jasinski, Oct 30 2008

Extensions

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

More terms from Amiram Eldar, Mar 31 2020

Status

approved