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 A096494 Largest value in period of continued fraction of square root of n-th prime. 2
 2, 2, 4, 4, 6, 6, 8, 8, 8, 10, 10, 12, 12, 12, 12, 14, 14, 14, 16, 16, 16, 16, 18, 18, 18, 20, 20, 20, 20, 20, 22, 22, 22, 22, 24, 24, 24, 24, 24, 26, 26, 26, 26, 26, 28, 28, 28, 28, 30, 30, 30, 30, 30, 30, 32, 32, 32, 32, 32, 32, 32, 34, 34, 34, 34, 34, 36, 36, 36, 36, 36, 36 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA It seems that limit n->infinity a(n)/n = 0. - Benoit Cloitre, Apr 19 2003 a(n) = 2*A000006(n). - Benoit Cloitre, Apr 19 2003 EXAMPLE n=31,p[31]=127: the period={3,1,2,2,7,11,7,2,2,1,3,22},a[31]=22; MAPLE A096491 := proc(n) if issqr(n) then sqrt(n) ; else numtheory[cfrac](sqrt(n), 'periodic', 'quotients') ; %[2] ; max(op(%)) ; end if; end proc: A096494 := proc(n) option remember ; A096491(ithprime(n)) ; end proc: # R. J. Mathar, Mar 18 2010 MATHEMATICA {te=Table[0, {m}], u=1}; Do[s=Max[Last[ContinuedFraction[Prime[n]^(1/2)]]]; te[[u]]=s; u=u+1, {n, 1, m}]; te a[n_]:=IntegerPart[Sqrt[Prime[n]]] 2 IntegerPart[Sqrt[#]]&/@Prime[Range[90]] (* Vincenzo Librandi, Aug 09 2015 *) PROG (Haskell) a096494 = (* 2) . a000006  -- Reinhard Zumkeller, Sep 20 2014 CROSSREFS Cf. A000006, A003285, A005980, A054269. Cf. A096491, A096492, A096493, A096495, A096496. Cf. A117767. Sequence in context: A079584 A179291 A004079 * A116568 A239933 A061106 Adjacent sequences:  A096491 A096492 A096493 * A096495 A096496 A096497 KEYWORD nonn AUTHOR Labos Elemer, Jun 29 2004 STATUS approved

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