A092290 Decimal expansion of solution to n/x = x-n for n = 7.

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

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 = 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 = x-n ==> 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 A356869 A099987

Adjacent sequences: A092287 A092288 A092289 * A092291 A092292 A092293

Keyword

easy,nonn,cons

Author

Felix Tubiana, Feb 05 2004

Status

approved