A146332 Numbers k such that the continued fraction of (1 + sqrt(k))/2 has period 7.

89, 109, 113, 137, 373, 389, 509, 653, 685, 797, 853, 925, 949, 997, 1009, 1105, 1145, 1165, 1261, 1493, 1997, 2309, 2621, 2677, 2885, 2941, 3133, 3277, 3445, 3653, 3797, 4325, 4505, 4745, 4825, 4973, 5353, 5429, 5765, 6305, 6437, 6845, 7085, 7373, 7817, 7873

Offset

1,1

Comments

For primes in this sequence see A146352.

Links

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

Example

a(4) = 137 because continued fraction of (1+sqrt(137))/2 = 6, 2, 1, 5, 5, 1, 2, 11, 2, 1, 5, 5, 1, 2, 11, 2, 1, 5, 5, 1, 2, 11 ... has period (2, 1, 5, 5, 1, 2, 11) length 7.

Maple

A146326 := proc(n) if not issqr(n) then numtheory[cfrac]( (1+sqrt(n))/2, 'periodic', 'quotients') ; nops(%[2]) ; else 0 ; fi; end: isA146332 := proc(n) RETURN(A146326(n) = 7) ; end: for n from 2 to 1100 do if isA146332(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]]] == 7 &]  (* Amiram Eldar, Mar 31 2020 *)

Crossrefs

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

Sequence in context: A215165 A157764 A032691 * A146352 A050956 A352540

Adjacent sequences: A146329 A146330 A146331 * A146333 A146334 A146335

Keyword

nonn

Author

Artur Jasinski, Oct 30 2008

Extensions

997 added by R. J. Mathar, Sep 06 2009

More terms from Amiram Eldar, Mar 31 2020

Status

approved