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A090038 a(n) = floor(1/({n*k}-{n*k}^2)) -1, where k = sqrt(2)-1 and {} is the fractional part. 1
3, 6, 4, 3, 14, 3, 10, 3, 4, 7, 3, 34, 3, 5, 4, 3, 24, 3, 7, 3, 3, 9, 3, 17, 3, 4, 5, 3, 82, 3, 6, 4, 3, 12, 3, 11, 3, 4, 6, 3, 58, 3, 5, 4, 3, 18, 3, 8, 3, 3, 8, 3, 21, 3, 4, 5, 3, 41, 3, 6, 4, 3, 10, 3, 13, 3, 4, 6, 3, 198, 3, 5, 4, 3, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(P(n)) = A002203(n), n>=2, where P=A000129 are the Pell numbers.

Example: a(29) = 82, where 29 = P(5) and 82 = A002203(5).

a(A002203(n)) = P(n), n>=3.

Example: a(34) = 12, where 34 = A002203(4) and 12 = P(4).

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(9) = 4. Take {n*k} with k = .414213...= sqrt(2) - 1. Then {9*.414...} = .727922...with (.727922...)*(1 - .727922...) = .1980515...Invert, taking floor = 5. Finally, subtract 1 = 4.

MAPLE

A090038 := proc(n)

    k := sqrt(2)-1 ;

    fn := fpart(n*k) ;

    1/fn/(1-fn);

    floor(%)-1 ;

end proc: # R. J. Mathar, May 11 2013

MATHEMATICA

Table[Floor[1/(FractionalPart[n*(Sqrt[2] - 1)] - FractionalPart[n*(Sqrt[2] - 1)]^2)] - 1, {n, 1, 100}] (* G. C. Greubel, Sep 27 2018 *)

PROG

(PARI) a(n) = floor(1/(frac(n*sqrt(2))-frac(n*sqrt(2))^2)) - 1; \\ Michel Marcus, Sep 28 2018

CROSSREFS

Cf. A090038, A002203, A089959, A089960, A089961.

Sequence in context: A140072 A187148 A105559 * A308291 A006464 A233825

Adjacent sequences:  A090035 A090036 A090037 * A090039 A090040 A090041

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Nov 20 2003

STATUS

approved

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Last modified February 22 05:38 EST 2020. Contains 332115 sequences. (Running on oeis4.)