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A271452 Decimal expansion of Hoffman's approximation to Pi. 1


%S 3,1,4,1,5,9,2,6,5,3,6,4,3,8,2,2,2,1,0,3,6,3,1,7,8,8,9,3,4,4,0,0,7,2,

%T 3,4,1,6,8,7,6,9,1,5,0,9,4,2,8,5,9,6,9,5,2,1,0,6,0,7,1,5,2,4,0,7,6,2,

%U 8,2,4,9,3,7,2,5,4,1,2,8,4,3,3,4,7,8,0,7,8,9,8,4,0,6,1,2,3,7,1,8,6,7,7,3,7

%N Decimal expansion of Hoffman's approximation to Pi.

%C The expression (Googol/11222.11122)^(1/193), with Googol fixed as 10^100, approximates Pi with an absolute error of about 5.4e-11. The 'symmetry' of the denominator, the fact that 193 is a prime, and the fact that it relates Pi with Googol make it a rare curiosity.

%H Stanislav Sykora, <a href="/A271452/b271452.txt">Table of n, a(n) for n = 1..1000</a>

%H D. W. Hoffman, <a href="http://www.jstor.org/stable/25653799">A Pi Curiosity</a>, College Mathematics Journal, 40 (2009), 399.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Googol.html">Googol</a

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Approximations_of_%CF%80">Approximations of Pi</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Googol">Googol</a>.

%e 3.141592653643822210363178893440072341687691509428596952106071524 ...

%o (PARI) (10^100/11222.11122)^(1/193)

%o (MAGMA) SetDefaultRealField(RealField(100)); (10^100/11222.11122)^(1/193); // _G. C. Greubel_, Nov 04 2018

%Y Cf. A000796, A244450.

%K nonn,cons

%O 1,1

%A _Stanislav Sykora_, Apr 08 2016

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