A181045 Decimal expansion of A060295/24.

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

Offset

17,3

Comments

This real number is close to the prime number 10939058860032031. Also, the only (single) integer values placed in the denominator that will generate 'near-integers' from this relation are the divisors of 24: 1, 2, 3, 4, 6, 8, 12, 24 (cf. A018253). A total of 64 'near-integers' can be obtained from generating powers (1-8) of A060295 and dividing each by one of the divisors of 24. Example: The last (64th) 'near-integer' is A060295^8 = 2.25698985492608864738884...99926422461218840012234... *10^139 (which is split by ... for brevity), the digits of which close to the decimal point are ...218840.012234... . While this does not quite look like a 'near-integer' this is where the pattern of 0's and 9's in the decimal tail cease in the case. See A166532.

Links

G. C. Greubel, Table of n, a(n) for n = 17..10000

Math Overflow, Questions [From Mark A. Thomas, Oct 02 2010]

M. A. Thomas, Math Ontological Basis of Quasi Fine-Tuning in Ghc Cosmologies, HAL preprint Id: hal-01232022, 2015.

Formula

Equals exp(Pi * sqrt(163))/24.

Example

A060295/24 = 10939058860032030.999999999999968753024883257737036639... This is almost the prime 10939058860032031.

Mathematica

E^(Pi Sqrt[163])/24
RealDigits[Exp[Pi Sqrt[163]]/24, 10, 100][[1]] (* G. C. Greubel, Feb 14 2018 *)

Prog

(PARI) exp(Pi*sqrt(163))/24 \\ G. C. Greubel, Feb 14 2018
(Magma) R:= RealField(); Exp(Pi*Sqrt(163))/24;

Crossrefs

Cf. A166528, A166529, A166530, A166531.

Sequence in context: A266559 A372837 A111971 * A242815 A155166 A159467

Adjacent sequences: A181042 A181043 A181044 * A181046 A181047 A181048

Keyword

cons,nonn

Author

Mark A. Thomas, Sep 30 2010

Status

approved