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%I #6 May 21 2014 20:18:33
%S 2,3,5,1,2,5,2,8,4,8,1,1,1,7,4,8,6,5,6,3,5,5,8,8,1,7,4,3,9,1,8,7,9,0,
%T 0,9,8,8,0,9,8,4,5,1,9,5,8,3,5,2,9,5,9,8,5,8,2,6,7,7,9,6,6,3,1,6,7,0,
%U 3,1,9,0,5,1,3,7,1,3,2,4,8,7,4,7,1,4,0,9,0,0,0,0,1,5,0,0,3,1,1,7
%N Decimal expansion of the Conway-Guy constant, a constant associated with Erdős' sum-distinct set constant.
%D J. H. Conway and R. K. Guy, “Sets of Natural Numbers with Distinct Sums,” Notices Amer. Math. Soc., vol. 15, 1968.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.28, p. 189.
%H W. F. Lunnon, <a href="http://dx.doi.org/10.1090/S0025-5718-1988-0917837-5">Integer sets with distinct subset-sums</a>, Math. Comp. 50 (1988), 297-320.
%e 0.23512528481117486563558817439187900988...
%t digits = 100; Clear[v, s]; v[n_] := v[n] = 2*v[n-1] - v[n-1 - Floor[1/2 + Sqrt[2*(n-1)]]]; v[0] = 0; v[1] = 1; s[k_] := s[k] = v[k]/2^k // N[#, digits + 5] &; s[dk = 250]; s[k = 2*dk]; While[RealDigits[s[k], 10, digits] != RealDigits[s[k - dk], 10, digits], Print["k = ", k]; k = k + dk]; RealDigits[s[k], 10, digits] // First
%Y Cf. A002083, A005255.
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, May 21 2014
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