A146331 Numbers k such that continued fraction of (1 + sqrt(k))/2 has period 6.

18, 19, 22, 38, 39, 44, 54, 57, 58, 59, 66, 68, 70, 74, 86, 102, 105, 107, 111, 112, 114, 115, 130, 131, 146, 147, 148, 150, 159, 164, 175, 178, 183, 186, 187, 198, 203, 253, 258, 260, 264, 267, 273, 275, 278, 294, 303, 308, 309, 326, 327, 330, 333, 341, 346

Offset

1,1

Comments

For primes in this sequence see A146351.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Example

a(2) = 19 because continued fraction of (1+sqrt(19))/2 = 2, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1 ... has period (1, 2, 8, 2, 1, 3) length 6.

Maple

A146326 := proc(n) if not issqr(n) then numtheory[cfrac]( (1+sqrt(n))/2, 'periodic', 'quotients') ; nops(%[2]) ; else 0 ; fi; end: isA146331 := proc(n) RETURN(A146326(n) = 6) ; end: for n from 2 to 380 do if isA146331(n) then printf("%d, ", n) ; fi; od: # R. J. Mathar, Sep 06 2009

Mathematica

cf6Q[n_]:=Module[{c=(1+Sqrt[n])/2}, !IntegerQ[c]&&Length[ContinuedFraction[ c][[2]]]==6]; Select[Range[400], cf6Q] (* Harvey P. Dale, May 30 2012 *)

Crossrefs

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

Sequence in context: A326540 A241267 A241848 * A308894 A031956 A095393

Adjacent sequences: A146328 A146329 A146330 * A146332 A146333 A146334

Keyword

nonn

Author

Artur Jasinski, Oct 30 2008

Extensions

39, 68, 150, 203, etc. added by R. J. Mathar, Sep 06 2009

Status

approved