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A334422 Decimal expansion of Pi/128. 2
2, 4, 5, 4, 3, 6, 9, 2, 6, 0, 6, 1, 7, 0, 2, 5, 9, 6, 7, 5, 4, 8, 9, 4, 0, 1, 4, 3, 1, 8, 7, 1, 1, 1, 6, 2, 8, 2, 7, 9, 0, 3, 8, 5, 9, 3, 2, 6, 1, 8, 0, 1, 4, 2, 2, 6, 3, 6, 6, 7, 5, 4, 6, 2, 7, 4, 0, 4, 8, 1, 5, 6, 7, 4, 1, 1, 1, 0, 0, 7, 8, 0, 1, 7, 8, 1, 5, 2, 2, 0, 7, 2, 9, 8, 5, 2, 8, 9, 5, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

-1,1

COMMENTS

Consider 4 circles inscribed in a square. Inscribe a square in each circle. And finally, inscribe 4 circles inside each four small squares. Totally we get 16 small circles. Pi/128 is the ratio of the area of any small circle to the area of the initial square. See the link.

Pi/8 (A019675) is the area ratio for the 16 small circles and the initial square.

Pi/128 is also the surface area of a sphere whose diameter is 1/sqrt(128). (Cf A222066). - Omar E. Pol, May 29 2020

LINKS

Table of n, a(n) for n=-1..98.

Kirill Ustyantsev, Geometric interpretation of Pi/128

FORMULA

Equals Sum_{k>=1} sin(k)^5*cos(k)^5/k. - Amiram Eldar, Jul 11 2020

EXAMPLE

0.02454369260617025967548940143187111628279038593261801422636675462740481567411...

MATHEMATICA

RealDigits[Pi/128, 10, 100][[1]] (* Amiram Eldar, Apr 30 2020 *)

PROG

(PARI)

default(realprecision, 100);

Pi/128

CROSSREFS

Cf. A000796, A019675, A222066.

Sequence in context: A123545 A123546 A339069 * A317499 A004581 A212790

Adjacent sequences:  A334419 A334420 A334421 * A334423 A334424 A334425

KEYWORD

nonn,cons

AUTHOR

Kirill Ustyantsev, Apr 30 2020

STATUS

approved

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Last modified August 5 07:54 EDT 2021. Contains 346464 sequences. (Running on oeis4.)