A332524 -id:A332524 - cp's OEIS frontend

A332506 Decimal expansion of the number snc(2 Pi), where snc is the sine-normal-to-cosine function; see A332500.

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

Offset: 1

Clark Kimberling, May 05 2020

			snc(2 Pi) = 5.544100173964425835269974678885...

Cf. A332500, A003957, A332523 (numerators of convergents), A332524 (denominators of convergents).

u = u /. FindRoot[ u + Cos[u] == 2 Pi, {u, 0}, WorkingPrecision -> 150]
RealDigits[u][[1]]

snc(2 Pi) = 2 Pi + snc(0), where snc(0) = Dottie number (A003957).

A332523 Numerators of convergents to 2*Pi + Dottie number (A332506).

Original entry on oeis.org

5, 6, 11, 61, 316, 377, 4463, 4840, 9303, 51355, 60658, 1628463, 3317584, 38121887, 41439471, 79561358, 200562187, 280123545, 760809277, 73317814137, 74078623414, 147396437551, 221475060965, 368871498516, 590346559481, 226471603779739, 1359419969237915

Offset: 0

Clark Kimberling, May 05 2020

Cf. A332524, A332506, A212112, A223957, A332500.

d = FindRoot[Cos[u] == 2 Pi - u, {u, 0, 1}, WorkingPrecision -> 10000][[1, -1]];
Numerator[Convergents[d, 100]]    (* A332523 *)
Denominator[Convergents[d, 100]]  (* A332524 *)

cp's OEIS Frontend

A332506 Decimal expansion of the number snc(2 Pi), where snc is the sine-normal-to-cosine function; see A332500.

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