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A146332
Numbers k such that the continued fraction of (1 + sqrt(k))/2 has period 7.
3
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
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 *)
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