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A127454 Decimal expansion of transcendental solution to round pegs in square holes problem. 2
8, 1, 3, 7, 9, 4, 1, 0, 4, 6, 0, 9, 1, 3, 7, 2, 3, 7, 6, 5, 2, 9, 8, 3, 8, 9, 8, 4, 0, 5, 3, 2, 2, 3, 3, 7, 0, 0, 9, 6, 7, 2, 5, 3, 0, 9, 7, 6, 2, 4, 4, 3, 7, 6, 9, 5, 8, 3, 5, 3, 0, 9, 9, 2, 2, 4, 6, 3, 0, 9, 4, 1, 2, 0, 5, 6, 6, 0, 1, 6, 0, 7, 7, 8, 7, 7, 6, 4, 2, 8, 6, 6, 5, 9, 8, 8, 9, 8, 1, 8, 8, 1, 3, 6, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This value "must be determined numerically. As a result, a round peg fits better into a square hole than a square peg fits into a round hole only for integer dimensions n < 9."

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..1001

David Singmaster, On Round Pegs in Square Holes and Square Pegs in Round Holes, Math. Mag. 37, 335-339, 1964.

Eric Weisstein's World of Mathematics, Peg.

FORMULA

Where the real number ratio crosses 1 in (Pi^n)(n^(n/2))/(2^(2n))(Gamma(1+n/2))^2. n such that (Pi^n)(n^(n/2)) = (2^(2n))(Gamma(1+n/2))^2.

EXAMPLE

8.13794104609137237652983898405322337009672530976244376958353099224630941205660...

MATHEMATICA

RealDigits[ FindRoot[ Pi^x*x^(x/2) == 2^(2 x) Gamma[1 + x/2]^2, {x, 8}, WorkingPrecision -> 121][[1, 2]], 10, 111][[1]] (* Robert G. Wilson v, Jul 03 2014 *)

CROSSREFS

Cf. A194940.

Sequence in context: A011391 A092515 A193032 * A093602 A011469 A140457

Adjacent sequences:  A127451 A127452 A127453 * A127455 A127456 A127457

KEYWORD

cons,nonn

AUTHOR

Jonathan Vos Post, Jan 13 2007

EXTENSIONS

More terms from Eric W. Weisstein, Jan 15 2007

STATUS

approved

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Last modified January 28 12:46 EST 2022. Contains 350656 sequences. (Running on oeis4.)