Search: a232735 -id:a232735
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A232736
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Decimal expansion of sin(Pi/14), or the imaginary part of (-1)^(1/7).
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+10
10
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2, 2, 2, 5, 2, 0, 9, 3, 3, 9, 5, 6, 3, 1, 4, 4, 0, 4, 2, 8, 8, 9, 0, 2, 5, 6, 4, 4, 9, 6, 7, 9, 4, 7, 5, 9, 4, 6, 6, 3, 5, 5, 5, 6, 8, 7, 6, 4, 5, 4, 4, 9, 5, 5, 3, 1, 1, 9, 8, 7, 0, 1, 5, 8, 9, 7, 4, 2, 1, 2, 3, 2, 0, 2, 8, 5, 4, 7, 3, 1, 9, 0, 7, 4, 5, 8, 1, 0, 5, 2, 6, 0, 8, 0, 7, 2, 9, 5, 6, 3, 4, 8, 7, 4, 7
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OFFSET
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0,1
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COMMENTS
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The corresponding real part is in A232735.
Root of the equation 1 - 4*x - 4*x^2 + 8*x^3 = 0. - Vaclav Kotesovec, Apr 04 2021
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LINKS
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FORMULA
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EXAMPLE
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0.222520933956314404288902564496794759466355568764544955311987...
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MATHEMATICA
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RealDigits[Cos[3*Pi/7], 10, 120][[1]] (* G. C. Greubel, Sep 04 2022 *)
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PROG
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(Magma) R:= RealField(120); Cos(3*Pi(R)/7); // G. C. Greubel, Sep 04 2022
(SageMath) numerical_approx(cos(3*pi/7), digits=120) # G. C. Greubel, Sep 04 2022
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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A232737
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Decimal expansion of the real part of I^(1/8), or cos(Pi/16).
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+10
5
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9, 8, 0, 7, 8, 5, 2, 8, 0, 4, 0, 3, 2, 3, 0, 4, 4, 9, 1, 2, 6, 1, 8, 2, 2, 3, 6, 1, 3, 4, 2, 3, 9, 0, 3, 6, 9, 7, 3, 9, 3, 3, 7, 3, 0, 8, 9, 3, 3, 3, 6, 0, 9, 5, 0, 0, 2, 9, 1, 6, 0, 8, 8, 5, 4, 5, 3, 0, 6, 5, 1, 3, 5, 4, 9, 6, 0, 5, 0, 6, 3, 9, 1, 5, 0, 6, 4, 9, 8, 5, 8, 5, 3, 3, 0, 0, 7, 6, 3, 2, 5, 9, 8, 9, 4
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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The corresponding imaginary part is in A232738.
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LINKS
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FORMULA
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EXAMPLE
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0.9807852804032304491261822361342390369739337308933360950029160885453...
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MATHEMATICA
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RealDigits[Cos[Pi/16], 10, 120][[1]] (* Amiram Eldar, Jun 29 2023 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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A343059
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Decimal expansion of tan(Pi/14).
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+10
3
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2, 2, 8, 2, 4, 3, 4, 7, 4, 3, 9, 0, 1, 4, 9, 9, 3, 8, 0, 7, 7, 6, 1, 1, 3, 6, 2, 0, 6, 1, 0, 1, 4, 7, 8, 2, 7, 3, 8, 7, 8, 1, 6, 8, 0, 9, 8, 0, 3, 5, 2, 6, 3, 7, 9, 7, 9, 6, 8, 8, 9, 1, 9, 6, 0, 3, 8, 2, 4, 8, 5, 5, 7, 1, 3, 8, 8, 1, 8, 7, 8, 9, 1, 4, 6, 9, 3, 8, 7, 0, 3, 7, 7, 1, 5, 5, 5, 6, 8, 2, 6, 0, 2, 7, 1, 5, 9, 7, 1, 7, 3, 5, 3, 4, 2, 5, 3, 8, 7
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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Root of the equation -1 + 21*x^2 - 35*x^4 + 7*x^6 = 0. - Vaclav Kotesovec, Apr 04 2021
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LINKS
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EXAMPLE
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0.228243474390149938077611362061014782...
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MATHEMATICA
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RealDigits[Tan[Pi/14], 10, 125][[1]] (* Amiram Eldar, Apr 27 2021 *)
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PROG
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(PARI) tan(Pi/14)
(SageMath) numerical_approx(tan(pi/14), digits=124) # G. C. Greubel, Sep 30 2022
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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A343056
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Decimal expansion of the real part of i^(1/16), or cos(Pi/32).
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+10
2
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9, 9, 5, 1, 8, 4, 7, 2, 6, 6, 7, 2, 1, 9, 6, 8, 8, 6, 2, 4, 4, 8, 3, 6, 9, 5, 3, 1, 0, 9, 4, 7, 9, 9, 2, 1, 5, 7, 5, 4, 7, 4, 8, 6, 8, 7, 2, 9, 8, 5, 7, 0, 6, 1, 8, 3, 3, 6, 1, 2, 9, 6, 5, 7, 8, 4, 8, 9, 0, 1, 6, 6, 8, 9, 4, 5, 8, 6, 5, 3, 7, 9, 7, 2, 5, 2, 9, 0, 8, 4, 2, 6, 9, 6, 4, 8, 3, 9, 0, 2, 8, 7, 7, 2, 4, 4, 9, 3, 1, 1, 8, 2, 9
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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LINKS
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FORMULA
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Equals (1/2) * sqrt(2+sqrt(2+sqrt(2+sqrt(2)))).
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EXAMPLE
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0.9951847266721968862448369...
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MATHEMATICA
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RealDigits[Cos[Pi/32], 10, 100][[1]] (* Amiram Eldar, Apr 27 2021 *)
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PROG
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(PARI) real(I^(1/16))
(PARI) cos(Pi/32)
(PARI) sqrt(2+sqrt(2+sqrt(2+sqrt(2))))/2
(Magma) R:= RealField(127); Cos(Pi(R)/32) // G. C. Greubel, Sep 30 2022
(SageMath) numerical_approx(cos(pi/32), digits=122) # G. C. Greubel, Sep 30 2022
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CROSSREFS
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cos(Pi/m): A010503 (m=4), A019863 (m=5), A010527 (m=6), A073052 (m=7), A144981 (m=8), A019879 (m=9), A019881 (m=10), A019884 (m=12), A232735 (m=14), A019887 (m=15), A232737 (m=16), A210649 (m=17), A019889 (m=18), A019890 (m=20), A144982 (m=24), A019893 (m=30). this sequence (m=32), A019894 (m=36).
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KEYWORD
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AUTHOR
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STATUS
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approved
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