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Decimal expansion of the Atkinson-Negro-Santoro constant, a constant associated with Erdős' sum-distinct set constant.
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%I #6 May 21 2014 20:18:25

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

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

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

%N Decimal expansion of the Atkinson-Negro-Santoro constant, a constant associated with Erdős' sum-distinct set constant.

%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 0.3166841736527058202183565723...

%t digits = 100; Clear[u, s]; u[n_] := u[n] = 2 u[n-1] - u[n-1 - Floor[(n-1)/2 + 1]]; u[0] = 0; u[1] = 1; s[k_] := s[k] = u[k]/2^k // N[#, digits + 5] &; s[dk = 100]; 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