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Search: a196818 -id:a196818
Displaying 1-5 of 5 results found. page 1
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A196816 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=cos(x). +10
7
1, 1, 0, 2, 5, 0, 5, 8, 2, 4, 4, 0, 6, 4, 1, 6, 0, 4, 3, 5, 7, 1, 0, 5, 0, 1, 5, 5, 0, 2, 2, 2, 2, 4, 0, 7, 3, 8, 8, 4, 8, 1, 0, 5, 8, 2, 0, 0, 9, 7, 7, 5, 1, 1, 6, 0, 8, 5, 3, 7, 5, 3, 7, 1, 4, 7, 6, 3, 5, 2, 2, 9, 5, 8, 5, 5, 8, 8, 3, 9, 6, 0, 3, 3, 1, 5, 5, 3, 6, 1, 0, 8, 1, 4, 9, 4, 8, 3, 2, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
Table of n, a(n) for n=1..100.
Eric Weisstein's World of Mathematics, Witch of Agnesi
EXAMPLE
x=1.10250582440641604357105015502222407388481058200...
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]
PROG
(PARI) solve(x=1, 1.5, cos(x)*(1+x^2) - 1) \\ Michel Marcus, Feb 10 2015
CROSSREFS
Cf. A196914, A196817, A196818, A196819, A196820, A196821.
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 06 2011
STATUS
approved
A196817 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=2*cos(x). +10
6
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.
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 06 2011
STATUS
approved
A196819 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=4*cos(x). +10
6
1, 4, 9, 3, 3, 1, 9, 5, 3, 5, 7, 3, 8, 2, 4, 2, 0, 1, 9, 2, 6, 6, 6, 7, 6, 1, 8, 4, 1, 7, 9, 8, 1, 8, 4, 0, 9, 6, 2, 5, 3, 4, 9, 9, 3, 6, 9, 7, 4, 1, 5, 8, 7, 8, 6, 6, 3, 7, 2, 7, 1, 3, 8, 7, 3, 4, 2, 0, 8, 4, 6, 1, 0, 8, 8, 1, 0, 1, 5, 7, 6, 7, 9, 2, 5, 5, 0, 3, 5, 7, 5, 2, 7, 0, 2, 8, 7, 1, 1, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Table of n, a(n) for n=1..100.
EXAMPLE
x=1.4933195357382420192666761841798184096253499369741587866...
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.
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 06 2011
STATUS
approved
A196820 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=5*cos(x). +10
6
1, 5, 0, 9, 7, 7, 1, 9, 0, 0, 4, 7, 0, 7, 2, 6, 8, 8, 5, 3, 5, 5, 4, 9, 3, 7, 5, 3, 5, 0, 0, 9, 8, 6, 5, 9, 9, 4, 4, 8, 6, 3, 7, 7, 2, 7, 5, 6, 3, 8, 3, 7, 3, 0, 5, 0, 6, 6, 8, 0, 5, 9, 3, 4, 3, 1, 5, 3, 7, 5, 3, 9, 5, 9, 0, 0, 9, 7, 0, 3, 7, 1, 1, 0, 9, 2, 9, 0, 8, 1, 2, 9, 7, 3, 8, 7, 9, 0, 2, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Table of n, a(n) for n=1..100.
EXAMPLE
x=1.50977190047072688535549375350098659944863772756...
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.
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 06 2011
STATUS
approved
A196821 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=6*cos(x). +10
6
1, 5, 2, 0, 4, 4, 9, 4, 5, 0, 8, 3, 3, 8, 1, 6, 3, 6, 3, 1, 4, 7, 4, 5, 8, 8, 2, 0, 8, 9, 0, 5, 6, 3, 9, 6, 3, 1, 3, 8, 9, 8, 5, 3, 0, 5, 5, 8, 3, 2, 7, 8, 4, 3, 5, 1, 8, 1, 2, 8, 9, 3, 4, 0, 1, 3, 6, 8, 8, 1, 5, 5, 1, 6, 1, 1, 3, 2, 8, 2, 2, 3, 1, 6, 8, 8, 9, 2, 6, 3, 2, 4, 0, 2, 9, 2, 6, 1, 3, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Table of n, a(n) for n=1..100.
EXAMPLE
x=1.5204494508338163631474588208905639631389853055832784...
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.
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 06 2011
STATUS
approved
page 1

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Last modified August 18 23:05 EDT 2024. Contains 375284 sequences. (Running on oeis4.)