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

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...

Mathematica

RealDigits[ Nest[ NextPrime[#^2, -1] &, 2, 8]^(2^-9), 10, 111][[1]]

Crossrefs

Cf. A051021, A059785, A112597, A117739.

Sequence in context: A369371 A242207 A060465 * A139339 A090986 A245221

Adjacent sequences: A219174 A219175 A219176 * A219178 A219179 A219180

Keyword

cons,nonn

Author

Robert G. Wilson v, Nov 15 2012

Status

approved