A393637 Decimal expansion of 2*sin(Pi/8)/(1+cos(Pi/8)).

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

Offset

0,1

Comments

Linear approximation of the type |h|=alpha*max(|x|,|y|)+beta*min(|x|,|y|) to the hypot function |h|=sqrt(x^2+y^2) attains the smallest maximum error when alpha = A393636 and beta is this constant. The absolute value of the minimax error of this approximation equals A393638.

Links

Table of n, a(n) for n=0..104.

Ara Abdulsatar Assim, ASIC implementation of high-speed vector magnitude & arctangent approximator, Computing, Telecommunication and Control, 14 (2021), 7-14.

Wikipedia, Alpha max plus beta min algorithm.

Formula

Equals 2*tan(Pi/16) = 2*A343060.

Example

0.39782473475931601382...

Mathematica

RealDigits[2*Tan[Pi/16], 10, 105][[1]] (* Amiram Eldar, Feb 24 2026 *)

Prog

(PARI) 2*sin(Pi/8)/(1+cos(Pi/8))

Crossrefs

Cf. A393636, A393638, A343060.

Sequence in context: A201943 A358614 A201760 * A046261 A074806 A010634

Adjacent sequences: A393634 A393635 A393636 * A393638 A393639 A393640

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Feb 23 2026

Status

approved