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 A090550 Decimal expansion of solution to n/x = x-n for n = 5. 12
 5, 8, 5, 4, 1, 0, 1, 9, 6, 6, 2, 4, 9, 6, 8, 4, 5, 4, 4, 6, 1, 3, 7, 6, 0, 5, 0, 3, 0, 9, 6, 9, 1, 4, 3, 5, 3, 1, 6, 0, 9, 2, 7, 5, 3, 9, 4, 1, 7, 2, 8, 8, 5, 8, 6, 4, 0, 6, 3, 4, 5, 8, 6, 8, 1, 1, 5, 7, 8, 1, 3, 8, 8, 4, 5, 6, 7, 0, 7, 3, 4, 9, 1, 2, 1, 6, 2, 1, 6, 1, 2, 5, 6, 8, 1, 7, 3, 4, 1, 2, 4 (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 = 5.  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 = 5: x = (5 + sqrt(45))/2 = 5.85410196624968454... Equals (5 + 3*sqrt(5))/2 = 1 + 3*phi = sqrt(5)*(phi)^2, where phi is the golden ratio. - G. C. Greubel, Jul 03 2017 EXAMPLE 5.85410196624968454... MATHEMATICA RealDigits[(5+3*Sqrt[5])/2, 10, 120][[1]] (* Harvey P. Dale, Nov 27 2013 *) PROG (PARI) (5 + 3*sqrt(5))/2 \\ G. C. Greubel, Jul 03 2017 CROSSREFS Cf. n+n/(n+n/(n+...)): A090388 (n=2), A090458 (n=3), A090488 (n=4), A092294 (n=6), A092290 (n=7), A090654 (n=8), A090655 (n=9), A090656 (n=10). - Stanislav Sykora, Jan 23 2014 Sequence in context: A300085 A186691 A199057 * A171819 A171541 A306204 Adjacent sequences:  A090547 A090548 A090549 * A090551 A090552 A090553 KEYWORD easy,nonn,cons AUTHOR Felix Tubiana (fat2(AT)columbia.edu), Feb 05 2004 STATUS approved

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Last modified June 19 23:01 EDT 2019. Contains 324222 sequences. (Running on oeis4.)