A349701 Decimal expansion of the smallest imaginary part of solutions z of cos(sin(z)) = sin(cos(z)).

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

Offset

0,1

Comments

Solutions of cos(sin(z)) = sin(cos(z)) are of the form z = 2 k Pi +- Pi/4 +- i*y, where k is an arbitrary integer, and y is the constant given here, or some larger value (2.399388..., 2.99286967..., 3.3619044...).

Links

Table of n, a(n) for n=0..84.

Formula

y = 0.4663385348278305845718632848784660354269560408360176474839528869636889462...

Maple

Digits:= 140:
abs(Im(fsolve(cos(sin(z))-sin(cos(z)), z, complex)));  # Alois P. Heinz, Nov 26 2021

Mathematica

RealDigits[Im[z /. FindRoot[Cos[Sin[z]] == Sin[Cos[z]], {z, Pi/4 + I/2}, WorkingPrecision -> 110]], 10, 100][[1]] (* Amiram Eldar, Nov 26 2021 *)

Prog

(PARI) A349701_upto(N)={localprec(N+5); my(x=Pi/4); digits(solve(y=.4, .5, real(cos(sin(x+I*y))-sin(cos(x+I*y))))\10^-N)}

Crossrefs

Cf. A003881 (Pi/4).

Sequence in context: A021686 A019923 A019800 * A344777 A191761 A201451

Adjacent sequences: A349698 A349699 A349700 * A349702 A349703 A349704

Keyword

nonn,cons

Author

M. F. Hasler, Nov 25 2021

Status

approved