

A092290


Decimal expansion of solution to n/x = xn for n = 7.


10



7, 8, 8, 7, 4, 8, 2, 1, 9, 3, 6, 9, 6, 0, 6, 1, 0, 3, 0, 2, 0, 3, 1, 9, 4, 1, 5, 3, 7, 0, 8, 1, 5, 4, 7, 8, 0, 4, 3, 7, 9, 3, 8, 4, 1, 3, 7, 7, 7, 2, 5, 1, 7, 9, 5, 4, 6, 3, 8, 4, 7, 8, 1, 4, 8, 9, 1, 3, 8, 2, 3, 2, 3, 1, 0, 9, 6, 5, 3, 1, 4, 0, 8, 3, 7, 8, 4, 6, 5, 7, 8, 5, 3, 4, 3, 5, 2, 8, 7, 7, 9
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OFFSET

1,1


COMMENTS

n/x = xn with n=1 gives the Golden Ratio = 1.6180339887...
Equals n +n/(n +n/(n +n/(n +....))) for n = 7. See also A090388.  Stanislav Sykora, Jan 23 2014


LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10001


FORMULA

n/x = xn ==> x^2  n*x  n = 0 ==> x = (n + sqrt(n^2 + 4*n)) / 2 (Positive Root) n = 7: x = (7 + sqrt(77))/2 = 7.88748219369606...


MATHEMATICA

RealDigits[(7+Sqrt[77])/2, 10, 50][[1]] (* G. C. Greubel, Jul 03 2017 *)


PROG

(PARI) (7+sqrt(77))/2 \\ Charles R Greathouse IV, Oct 18 2012


CROSSREFS

Cf. n+n/(n+n/(n+...)): A090388 (n=2), A090458 (n=3), A090488 (n=4), A090550 (n=5), A092294 (n=6), A090654 (n=8), A090655 (n=9), A090656 (n=10).  Stanislav Sykora, Jan 23 2014
Sequence in context: A085361 A256781 A248224 * A156571 A099987 A226320
Adjacent sequences: A092287 A092288 A092289 * A092291 A092292 A092293


KEYWORD

easy,nonn,cons


AUTHOR

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


STATUS

approved



