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A257945 Decimal expansion of abs(i/(i + i/(i + i/...))) and abs(i/(1 + i/(1 + i/...))), i being the imaginary unit. 1
6, 9, 3, 2, 0, 5, 4, 6, 4, 6, 2, 3, 7, 9, 7, 3, 2, 0, 4, 3, 4, 3, 6, 3, 7, 0, 4, 2, 2, 4, 1, 3, 8, 6, 8, 7, 9, 4, 1, 0, 2, 1, 7, 5, 0, 1, 6, 9, 2, 1, 9, 0, 1, 3, 3, 9, 9, 5, 5, 5, 8, 6, 7, 5, 2, 9, 5, 5, 8, 1, 4, 8, 8, 3, 1, 6, 6, 1, 0, 4, 3, 0, 2, 2, 3, 3, 6, 0, 6, 9, 1, 5, 2, 6, 8, 1, 8, 5, 8, 3, 5, 0, 5, 6, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Set v = A156590 and u = (A156548 - 1). Then the continued fractions evaluate to i/(i + i/(i + i/...)) = (sqrt(4*i - 1) - i)/2 = v + u*i and i/(1 + i/(1 + i/...)) = (sqrt(4*i + 1) - 1)/2 = u + v*i. They can be evaluated either explicitly or as limits of the convergent recursive mappings z -> i/(i + z) and z -> i/(1 + z), respectively, starting, for example, with z = 0.

An algebraic integer of degree 8. - Charles R Greathouse IV, Jun 02 2015

LINKS

Stanislav Sykora, Table of n, a(n) for n = 0..2000

FORMULA

Equals sqrt(1 + sqrt(17) - sqrt(2*(1 + sqrt(17))))/2.

EXAMPLE

0.69320546462379732043436370422413868794102175016921901339955586752...

MATHEMATICA

RealDigits[Sqrt[1 + Sqrt[17] - Sqrt[2*(1 + Sqrt[17])]]/2, 10, 105][[1]] (* Vaclav Kotesovec, Jun 02 2015 *)

PROG

(PARI) sqrt(1+sqrt(17)-sqrt(2*(1+sqrt(17))))/2

(PARI) polrootsreal(x^8-x^6-2*x^4-x^2+1)[3] \\ Charles R Greathouse IV, Jun 02 2015

CROSSREFS

Cf. A156548, A156590.

Sequence in context: A022698 A013707 A002162 * A271526 A072365 A239068

Adjacent sequences:  A257942 A257943 A257944 * A257946 A257947 A257948

KEYWORD

nonn,cons

AUTHOR

Stanislav Sykora, May 29 2015

STATUS

approved

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Last modified March 27 02:08 EDT 2017. Contains 284143 sequences.