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Search: a069997 -id:a069997
Displaying 1-6 of 6 results found.
page 1
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A196407
Decimal expansion of the least positive number x satisfying e^(-x)=2*sin(x).
+10
6
3, 5, 7, 3, 2, 7, 4, 1, 1, 3, 2, 2, 5, 5, 5, 4, 8, 0, 8, 3, 1, 4, 2, 4, 6, 7, 4, 8, 1, 2, 1, 1, 2, 3, 0, 9, 7, 1, 2, 8, 2, 7, 8, 2, 2, 4, 8, 3, 0, 5, 6, 6, 1, 0, 1, 8, 3, 6, 4, 3, 0, 8, 6, 0, 7, 7, 5, 4, 3, 8, 0, 5, 1, 4, 6, 5, 6, 3, 9, 8, 4, 0, 4, 3, 7, 5, 8, 8, 0, 5, 0, 8, 3, 9, 1, 8, 4, 7, 9, 1
(list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
Table of n, a(n) for n=0..99.
EXAMPLE
x=0.3573274113225554808314246748121123097128278224830566...
MATHEMATICA
Plot[{E^(-x), Sin[x], 2 Sin[x], 3 Sin[x], 4 Sin[x]}, {x, 0, Pi/2}]
t = x /. FindRoot[E^(-x) == Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* Cf. A069997 *)
t = x /. FindRoot[E^(-x) == 2 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196407 *)
t = x /. FindRoot[E^(-x) == 3 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196408 *)
t = x /. FindRoot[E^(-x) == 4 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196409 *)
t = x /. FindRoot[E^(-x) == 5 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196462 *)
t = x /. FindRoot[E^(-x) == 6 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196463 *)
CROSSREFS
Cf. A196396, A196401.
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 02 2011
STATUS
approved
A196408
Decimal expansion of the least positive number x satisfying e^(-x)=3*sin(x).
+10
5
2, 5, 9, 9, 4, 8, 2, 1, 3, 5, 3, 3, 2, 1, 2, 8, 0, 6, 6, 7, 7, 5, 2, 2, 6, 3, 6, 8, 4, 6, 3, 2, 6, 7, 9, 8, 9, 3, 8, 7, 1, 9, 2, 3, 9, 6, 3, 5, 6, 3, 6, 8, 3, 4, 5, 3, 1, 2, 4, 9, 4, 4, 3, 2, 0, 9, 9, 5, 9, 2, 1, 6, 4, 6, 2, 2, 5, 4, 7, 3, 4, 3, 9, 1, 5, 0, 0, 3, 4, 1, 4, 5, 8, 5, 0, 8, 4, 8, 7, 3, 9
(list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
Table of n, a(n) for n=0..100.
EXAMPLE
x=0.259948213533212806677522636846326798938719239635636...
MATHEMATICA
Plot[{E^(-x), Sin[x], 2 Sin[x], 3 Sin[x], 4 Sin[x]}, {x, 0, Pi/2}]
t = x /. FindRoot[E^(-x) == Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* Cf. A069997 *)
t = x /. FindRoot[E^(-x) == 2 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196407 *)
t = x /. FindRoot[E^(-x) == 3 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196408 *)
t = x /. FindRoot[E^(-x) == 4 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196409 *)
t = x /. FindRoot[E^(-x) == 5 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196462 *)
t = x /. FindRoot[E^(-x) == 6 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196463 *)
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 02 2011
STATUS
approved
A196409
Decimal expansion of the least positive number x satisfying e^(-x)=4*sin(x).
+10
5
2, 0, 5, 0, 8, 0, 0, 4, 4, 5, 3, 9, 2, 9, 1, 6, 4, 4, 4, 5, 6, 0, 5, 1, 2, 9, 0, 8, 9, 3, 4, 7, 2, 3, 6, 2, 4, 7, 6, 2, 0, 8, 2, 0, 9, 1, 7, 7, 7, 1, 3, 6, 9, 6, 5, 8, 7, 3, 3, 5, 7, 9, 0, 1, 4, 5, 5, 8, 2, 8, 0, 3, 8, 1, 0, 9, 5, 8, 6, 4, 0, 4, 8, 5, 6, 3, 1, 3, 5, 5, 4, 7, 8, 3, 5, 7, 2, 3, 3, 2
(list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
Table of n, a(n) for n=0..99.
EXAMPLE
x=0.205080044539291644456051290893472362476208209177713696...
MATHEMATICA
Plot[{E^(-x), Sin[x], 2 Sin[x], 3 Sin[x], 4 Sin[x]}, {x, 0, Pi/2}]
t = x /. FindRoot[E^(-x) == Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* Cf. A069997 *)
t = x /. FindRoot[E^(-x) == 2 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196407 *)
t = x /. FindRoot[E^(-x) == 3 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196408 *)
t = x /. FindRoot[E^(-x) == 4 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196409 *)
t = x /. FindRoot[E^(-x) == 5 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196462 *)
t = x /. FindRoot[E^(-x) == 6 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196463 *)
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 02 2011
STATUS
approved
A196462
Decimal expansion of the least positive number x satisfying e^(-x)=5*sin(x).
+10
5
1, 6, 9, 6, 1, 0, 7, 1, 3, 6, 3, 6, 7, 3, 4, 8, 2, 1, 7, 3, 3, 3, 1, 9, 8, 7, 1, 3, 9, 9, 3, 4, 0, 9, 4, 4, 0, 6, 4, 0, 2, 3, 1, 1, 9, 6, 0, 5, 7, 7, 2, 1, 7, 9, 4, 9, 0, 5, 1, 4, 3, 5, 7, 7, 6, 8, 8, 8, 0, 9, 3, 8, 6, 5, 4, 4, 8, 2, 0, 7, 3, 2, 3, 4, 2, 0, 0, 1, 8, 6, 7, 5, 9, 0, 8, 5, 9, 0, 9, 7
(list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Table of n, a(n) for n=0..99.
EXAMPLE
x=0.1696107136367348217333198713993409440640231196057...
MATHEMATICA
Plot[{E^(-x), Sin[x], 2 Sin[x], 3 Sin[x], 4 Sin[x]}, {x, 0, Pi/2}]
t = x /. FindRoot[E^(-x) == Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* Cf. A069997 *)
t = x /. FindRoot[E^(-x) == 2 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196407 *)
t = x /. FindRoot[E^(-x) == 3 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196408 *)
t = x /. FindRoot[E^(-x) == 4 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196409 *)
t = x /. FindRoot[E^(-x) == 5 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196462 *)
t = x /. FindRoot[E^(-x) == 6 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196463 *)
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 02 2011
STATUS
approved
A196463
Decimal expansion of the least positive number x satisfying e^(-x)=6*sin(x).
+10
5
1, 4, 4, 7, 1, 5, 9, 3, 6, 6, 5, 1, 7, 2, 5, 9, 5, 1, 9, 2, 9, 1, 0, 9, 5, 3, 4, 3, 1, 9, 4, 4, 9, 2, 0, 1, 9, 9, 7, 3, 1, 8, 2, 8, 6, 8, 8, 5, 8, 0, 0, 7, 9, 6, 8, 0, 1, 7, 0, 0, 2, 6, 0, 6, 2, 0, 8, 4, 3, 4, 7, 2, 3, 4, 2, 4, 5, 5, 5, 0, 4, 8, 6, 5, 3, 9, 5, 0, 5, 9, 4, 2, 2, 3, 8, 1, 2, 2, 1, 9
(list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Table of n, a(n) for n=0..99.
EXAMPLE
x=0.144715936651725951929109534319449201997318286885800796...
MATHEMATICA
Plot[{E^(-x), Sin[x], 2 Sin[x], 3 Sin[x], 4 Sin[x]}, {x, 0, Pi/2}]
t = x /. FindRoot[E^(-x) == Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* Cf. A069997 *)
t = x /. FindRoot[E^(-x) == 2 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196407 *)
t = x /. FindRoot[E^(-x) == 3 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196408 *)
t = x /. FindRoot[E^(-x) == 4 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196409 *)
t = x /. FindRoot[E^(-x) == 5 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196462 *)
t = x /. FindRoot[E^(-x) == 6 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196463 *)
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 02 2011
STATUS
approved
A104780
Decimal expansion of solution to sin(x)-exp(-x)=0 around Pi.
+10
0
3, 0, 9, 6, 3, 6, 3, 9, 3, 2, 4, 1, 0, 6, 4, 6, 1, 1, 5, 6, 2, 5, 8, 4, 0, 8, 4, 9, 9, 0, 4, 0, 2, 4, 8, 5, 6, 5, 3, 2, 9, 1, 8, 6, 4, 1, 7, 5, 6, 2, 7, 7, 8, 0, 8, 0, 0, 5, 3, 2, 0, 8, 9, 6, 1, 3, 9, 4, 5, 8, 4, 7, 9, 5, 7, 2, 0, 0, 1, 5, 7, 3, 8, 0, 1, 7, 5, 2, 2, 2, 8, 3, 8, 1, 9, 9, 9, 3, 0, 7, 7, 5, 8, 1, 2
(list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Table of n, a(n) for n=1..105.
FORMULA
x=3.0963639324106461...
MATHEMATICA
RealDigits[ FindRoot[Sin[x] - Exp[ -x] == 0, {x, Pi}, WorkingPrecision -> 2^7][[1, 2]]][[1]] (* Robert G. Wilson v, Mar 26 2005 *)
CROSSREFS
Cf. A069997.
KEYWORD
cons,nonn
AUTHOR
Zak Seidov, Mar 25 2005
EXTENSIONS
More terms from Robert G. Wilson v, Mar 26 2005
STATUS
approved
page 1

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