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%I #9 Oct 31 2019 05:30:41
%S 3,4,4,9,3,5,8,8,9,0,2,5,9,7,4,0,4,1,5,9,5,1,3,2,1,8,5,1,2,5,3,8,8,8,
%T 3,6,0,3,4,5,6,2,4,5,0,3,8,2,5,4,1,5,9,1,0,8,8,1,4,9,4,1,0,0,5,7,5,5,
%U 6,9,6,0,6,8,8,7,2,1,0,1,3,5,7,0,3,7,6,9,4,2,8,5,9,6,1,3,3,6,0,8,8,1,9,8,1
%N Decimal expansion of y_4, the last of four non-explicit constants recursively derived from Khintchine's [Khinchin's] constant.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.8.1 Alternative representations [of real numbers], p. 63.
%H Herman P. Robinson, <a href="http://www.escholarship.org/uc/item/2t95c0bp">Mathematical Constants.</a>
%e 3.4493588902597404159513218512538883603456245038254159108814941005755696...
%t K = Khinchin; a[0] = pi[0] = 3; pi[n_] := Product[a[i], {i, 0, n}]; Clear[a]; a[n_?EvenQ] := a[n] = Ceiling[K^(n+1)/pi[n-1]]; a[n_?OddQ] := a[n] = Floor[K^(n+1)/pi[n-1]]; FromContinuedFraction[Array[a, 300, 0]] // RealDigits[#, 10, 105]& // First
%Y Cf. A002210, A245255, A245256, A245257.
%K nonn,cons
%O 1,1
%A _Jean-François Alcover_, Jul 15 2014
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