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 A146331 Numbers k such that continued fraction of (1 + sqrt(k))/2 has period 6. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 7 21:37 EST 2023. Contains 367662 sequences. (Running on oeis4.)