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%I #18 Apr 19 2024 02:00:32
%S 1,7,3,2,0,5,1,2,8,2,0,5,1,2,8,2,0,5,1,2,8,2,0,5,1,2,8,2,0,5,1,2,8,2,
%T 0,5,1,2,8,2,0,5,1,2,8,2,0,5,1,2,8,2,0,5,1,2,8,2,0,5,1,2,8,2,0,5,1,2,
%U 8,2,0,5,1,2,8,2,0,5,1,2,8,2,0,5,1,2,8,2
%N Decimal expansion of 1351/780.
%C This constant is the greater limit to the value of sqrt(3) used by Archimedes in the calculation of Pi.
%D Ernst Sondheimer and Alan Rogerson, Numbers and Infinity, Cambridge University Press, 1981, p. 97.
%H MathPages, <a href="https://mathpages.com/home/kmath038/kmath038.htm">Archimedes and the square root of 3</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1,-1,1).
%F From _Chai Wah Wu_, Apr 18 2024: (Start)
%F a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) for n > 8.
%F G.f.: x*(-5*x^7 + 10*x^6 - 10*x^5 + 5*x^4 - 5*x^3 + 3*x^2 - 6*x - 1)/((x - 1)*(x^2 - x + 1)*(x^2 + x + 1)). (End)
%e 1.732051282051282051282051282051282051282...
%t First[RealDigits[N[1351/780,88]]]
%Y Cf. A002194, A355673 (lesser limit), essentially the same as A021316.
%K nonn,cons,easy
%O 1,2
%A _Stefano Spezia_, Jul 14 2022
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