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 A248752 Decimal expansion of limit of the imaginary part of f(1-i,n)/f(1-i,n+1), where f(x,n) is the n-th Fibonacci polynomial. 7
 2, 5, 7, 0, 6, 5, 8, 6, 4, 1, 2, 1, 6, 7, 7, 1, 6, 0, 9, 0, 8, 5, 6, 8, 0, 6, 2, 0, 5, 2, 7, 3, 3, 7, 1, 8, 9, 0, 3, 7, 5, 7, 0, 0, 7, 9, 9, 8, 8, 1, 3, 4, 9, 4, 5, 2, 4, 1, 3, 0, 7, 9, 3, 7, 8, 0, 9, 4, 2, 2, 3, 6, 0, 4, 3, 1, 2, 1, 4, 5, 0, 9, 4, 0, 7, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The analogous limit of f(1,n)/f(1,n+1) is the golden ratio (A001622), LINKS FORMULA Equals (1-sqrt(sqrt(5)-2))/2. - Vaclav Kotesovec, Oct 19 2014 From Wolfdieter Lang, Mar 02 2018: (Start) Equals (1 - (2 - phi)*sqrt(phi))/2, with phi = A001622. Equals (1/10)*y*(1 - (1/50)*y^2) with y = A300070. (End) EXAMPLE limit = 0.2570658641216771609085680620527337189037570... Let q(x,n) = f(x,n)/f(x,n+1) and c = 1-i. n   f(n,x)                 Re(q(c,n))       Im(q(c,n))) 1    1                     1/2              1/2 2    x                     3/5              1/5 3    1 + x^2               1/2              1/4 4    2x + x^3              8/15             4/15 5    1 + 3 x^2 + x^4       69/130           33/130 Re(q(11,1+i) = 5021/9490 = 0.5290832... Im(q(11,1+i) = 4879/18980 = 0.275060... MAPLE evalf((1-sqrt(sqrt(5)-2))/2, 120); # Vaclav Kotesovec, Oct 19 2014 MATHEMATICA z = 300; t = Table[Fibonacci[n, x]/Fibonacci[n + 1, x], {n, 1, z}]; u = t /. x -> 1 - I; d1 = N[Re[u][[z]], 130] d2 = N[Im[u][[z]], 130] r1 = RealDigits[d1]  (* A248751 *) r2 = RealDigits[d2]  (* A248752 *) CROSSREFS Cf. A248750, A248751, A102426, A001622, A300070. Sequence in context: A231364 A025123 A071791 * A021393 A181583 A010589 Adjacent sequences:  A248749 A248750 A248751 * A248753 A248754 A248755 KEYWORD nonn,easy,cons AUTHOR Clark Kimberling, Oct 13 2014 STATUS approved

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Last modified November 28 12:22 EST 2021. Contains 349401 sequences. (Running on oeis4.)