A219177 - OEIS

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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.

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

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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

Robert G. Wilson v, Table of n, a(n) for n = 1..1000

EXAMPLE

=1.2720196331921934958697353209119288376375630826996476481322580415...