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
Examples
8.13794104609137237652983898405322337009672530976244376958353099224630941205660...
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.
Crossrefs
Cf. A194940.
Programs
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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 *)
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.
Extensions
More terms from Eric W. Weisstein, Jan 15 2007
Comments