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

%I A127454 #21 Feb 16 2025 08:33:04
%S A127454 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,
%T A127454 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,
%U A127454 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
%N A127454 Decimal expansion of transcendental solution to round pegs in square holes problem.
%C A127454 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."
%H A127454 Robert G. Wilson v, <a href="/A127454/b127454.txt">Table of n, a(n) for n = 1..1001</a>
%H A127454 David Singmaster, <a href="http://www.jstor.org/stable/2689251">On Round Pegs in Square Holes and Square Pegs in Round Holes</a>, Math. Mag. 37, 335-339, 1964.
%H A127454 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Peg.html">Peg.</a>
%F A127454 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.
%e A127454 8.13794104609137237652983898405322337009672530976244376958353099224630941205660...
%t A127454 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 *)
%Y A127454 Cf. A194940.
%K A127454 cons,nonn
%O A127454 1,1
%A A127454 _Jonathan Vos Post_, Jan 13 2007
%E A127454 More terms from _Eric W. Weisstein_, Jan 15 2007