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Decimal expansion of y_3, the third of four non-explicit constants recursively derived from Khintchine's [Khinchin's] constant.
3

%I #9 Oct 31 2019 05:30:32

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

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

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

%N Decimal expansion of y_3, the third 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 2.224751480980583015375598924924190424236366707982466701694563315747...

%t K = Khinchin; a[0] = pi[0] = 2; pi[n_] := Product[a[i], {i, 0, n}]; Clear[a]; a[n_?EvenQ] := a[n] = Floor[K^(n+1)/pi[n-1]]; a[n_?OddQ] := a[n] = Ceiling[K^(n+1)/pi[n-1]]; FromContinuedFraction[Array[a, 300, 0]] // RealDigits[#, 10, 105]& // First

%Y Cf. A002210, A245255, A245256, A245258.

%K nonn,cons

%O 1,1

%A _Jean-François Alcover_, Jul 15 2014