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%I #20 Aug 06 2017 22:38:27
%S 1,2,7,2,0,1,9,6,3,3,1,9,2,1,9,3,4,9,5,8,6,9,7,3,5,3,2,0,9,1,1,9,2,8,
%T 8,3,7,6,3,7,5,6,3,0,8,2,6,9,9,6,4,7,6,4,8,1,3,2,2,5,8,0,4,1,5,4,8,7,
%U 5,3,2,8,1,4,2,6,4,3,3,7,5,6,4,0,7,3,8,4,8,8,1,5,0,4,5,1,8,7,5,4,0,7,4,0,2,8
%N Decimal expansion of what appears to be the smallest possible C for which the nearest integer to C^2^n is always prime and starts with 2.
%C The square of this constant, C^2 = 1.6180339472264..., is very close to the Golden Ratio Phi (A001622).
%C This constant is about 3% less than Mills's constant, 1.306377883863..., (A051021).
%C Since there is always a prime between an integer and its square, this constant should satisfy the same criteria as does Mills's constant (A051021).
%C This constant, C, produces A059785.
%H Robert G. Wilson v, <a href="/A219177/b219177.txt">Table of n, a(n) for n = 1..1000</a>
%e =1.2720196331921934958697353209119288376375630826996476481322580415...
%t RealDigits[ Nest[ NextPrime[#^2, -1] &, 2, 8]^(2^-9), 10, 111][[1]]
%Y Cf. A051021, A059785, A112597, A117739.
%K cons,nonn
%O 1,2
%A _Robert G. Wilson v_, Nov 15 2012
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