A127454 Decimal expansion of transcendental solution to round pegs in square holes problem.

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

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,changed

Author

Jonathan Vos Post, Jan 13 2007

Extensions

More terms from Eric W. Weisstein, Jan 15 2007

Status

approved