A196817 - OEIS

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A196817

Decimal expansion of the least x>0 satisfying 1/(1+x^2)=2*cos(x).

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..100.

EXAMPLE

x=1.401269207599957942927187243790834191530882865453360260...

MATHEMATICA

Plot[{1/(1 + x^2), Cos[x], 2 Cos[x], 3 Cos[x], 4 Cos[x]}, {x, 0, 2}]

t = x /. FindRoot[1 == (1 + x^2) Cos[x], {x, 1, 1.5}, WorkingPrecision -> 100]

RealDigits[t] (* A196816 *)

t = x /. FindRoot[1 == 2 (1 + x^2) Cos[x], {x, 1, 1.6},

WorkingPrecision -> 100]

RealDigits[t] (* A196817 *)

t = x /. FindRoot[1 == 3 (1 + x^2) Cos[x], {x, 1, 1.6},

WorkingPrecision -> 100]

RealDigits[t] (* A196818 *)

t = x /. FindRoot[1 == 4 (1 + x^2) Cos[x], {x, 1, 1.6},

WorkingPrecision -> 100]

RealDigits[t] (* A196819 *)

t = x /. FindRoot[1 == 5 (1 + x^2) Cos[x], {x, 1, 1.6},

WorkingPrecision -> 100]

RealDigits[t] (* A196820 *)

t = x /. FindRoot[1 == 6 (1 + x^2) Cos[x], {x, 1, 1.6},

WorkingPrecision -> 100]

RealDigits[t] (* A196821 *)

CROSSREFS

Cf. A196914.

Sequence in context: A198637 A365094 A179296 * A229987 A343953 A307769

Adjacent sequences: A196814 A196815 A196816 * A196818 A196819 A196820

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 06 2011

STATUS

approved