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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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Last modified November 21 17:44 EST 2017. Contains 295004 sequences.