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URL: https://oeis.org/A215833

⇱ A215833 - OEIS

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A215833
Decimal expansion of the maximum value p > 0, such that (cos(sin(x)))^p >= sin(cos(x)), x in (0,Pi/2).
7
1, 5, 6, 0, 0, 1, 5, 5, 8, 3, 4, 5, 2, 4, 8, 3, 5, 8, 3, 2, 3, 1, 2, 0, 4, 1, 0, 7, 5, 3, 6, 9, 1, 7, 3, 4, 4, 8, 1, 6, 2, 2, 4, 2, 9, 1, 9, 1, 1, 5, 6, 6, 5, 4, 7, 6, 7, 0, 1, 0, 6, 4, 5, 9, 5, 5, 7, 0, 4, 2, 2, 2, 3, 0, 1, 9, 6, 7, 0, 0, 4, 9, 5, 4, 0, 2, 2, 9, 7, 9, 7, 3, 8, 1, 6, 8, 5, 8, 5, 2, 0, 5, 0, 9, 4, 0, 5, 1, 8, 8, 8, 7, 0, 2, 0, 3, 4, 2, 3, 9, 7, 1, 6, 4, 8
OFFSET
1,2
COMMENTS
Equal to the inverse of the maximum of the function f(x) from A215832.
LINKS
Roman Wituła, Danuta Jama, Edyta Hetmaniok, and Damian Słota, On some inequality of the trygonometric type, Zeszyty Naukowe Politechniki Slaskiej - Matematyka-Fizyka (Science Fascicle of Silesian Technical University - Math.-Phys.), 92 (2010), 83-92.
FORMULA
max p = 1/A215832 = 1.56001558345248358323120410753691734481622429191156...
MATHEMATICA
RealDigits[1 /Maximize[Log[Cos[Sin[x]]]/Log[Sin[Cos[x]]], {x}, WorkingPrecision -> 130][[1]]][[1]] (* Amiram Eldar, Mar 27 2026 *)
PROG
(PARI) f(x) = log(cos(sin(x)))/log(sin(cos(x)));
1 / f(solve(r = 4/5, 1, derivnum(x = r, f(x)))) \\ Amiram Eldar, Mar 27 2026
CROSSREFS
KEYWORD
nonn,cons,changed
AUTHOR
Roman Witula, Aug 24 2012
EXTENSIONS
a(14) onward corrected by Amiram Eldar, Mar 27 2026
STATUS
approved