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A219177
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.
2
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, 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, 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
OFFSET
1,2
COMMENTS
The square of this constant, C^2 = 1.6180339472264..., is very close to the Golden Ratio Phi (A001622).
This constant is about 3% less than Mills's constant, 1.306377883863..., (A051021).
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).
This constant, C, produces A059785.
LINKS
EXAMPLE
=1.2720196331921934958697353209119288376375630826996476481322580415...
MATHEMATICA
RealDigits[ Nest[ NextPrime[#^2, -1] &, 2, 8]^(2^-9), 10, 111][[1]]
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Robert G. Wilson v, Nov 15 2012
STATUS
approved