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A090655 Decimal expansion of solution to n/x = x-n for n = 9. 9
9, 9, 0, 8, 3, 2, 6, 9, 1, 3, 1, 9, 5, 9, 8, 3, 9, 3, 9, 6, 7, 8, 8, 3, 1, 9, 0, 1, 2, 0, 5, 7, 4, 3, 9, 1, 9, 3, 7, 6, 9, 4, 4, 8, 6, 0, 7, 6, 7, 8, 6, 9, 3, 1, 9, 0, 6, 5, 6, 7, 9, 5, 8, 4, 3, 4, 0, 7, 5, 0, 4, 2, 2, 4, 3, 9, 5, 1, 5, 6, 6, 7, 8, 0, 6, 9, 2, 8, 6, 2, 3, 0, 2, 7, 7, 3, 6, 0, 7, 6, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

n/x = x-n with n=1 gives the Golden Ratio = 1.6180339887...

Equals n +n/(n +n/(n +n/(n +....))) for n = 9. See also A090388. - Stanislav Sykora, Jan 23 2014

LINKS

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

FORMULA

n/x = x-n ==> x^2 - n*x - n = 0 ==> x = (n + sqrt(n^2 + 4*n)) / 2 (Positive Root) n = 9: x = (9 + sqrt(117))/2 = 9.90832691319598...

Equals (3/2)*(3 + sqrt(13)). - G. C. Greubel, Jul 03 2017

EXAMPLE

9.90832691319598...

MATHEMATICA

RealDigits[(3/2)*(3+Sqrt[13]), 10, 50][[1]] (* G. C. Greubel, Jul 03 2017 *)

PROG

(PARI) (3/2)*(3 + sqrt(13)) \\ G. C. Greubel, Jul 03 2017

CROSSREFS

Cf. n+n/(n+n/(n+...)): A090388 (n=2), A090458 (n=3), A090488 (n=4), A090550 (n=5), A092294 (n=6), A092290 (n=7), A090654 (n=8), A090656 (n=10). - Stanislav Sykora, Jan 23 2014

Sequence in context: A199960 A257176 A324859 * A334480 A229758 A076115

Adjacent sequences:  A090652 A090653 A090654 * A090656 A090657 A090658

KEYWORD

easy,nonn,cons

AUTHOR

Felix Tubiana (fat2(AT)columbia.edu), Feb 05 2004

STATUS

approved

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Last modified May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)