A166530 Decimal expansion of exp(4*Pi*sqrt(163)) (or A060295^4).

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

Offset: 70

Author

Mark A. Thomas, Oct 16 2009

Keywords

• nonn
• cons

Comments

Near-integer obtained by taking Ramanujan's constant e^(Pi*sqrt(163)) to the fourth power.

Examples

			exp^(4*Pi*sqrt(163)) = 47507787308251777254639209489097266182144917180394713663187474063...
		

References

• Henri Cohen, 'A Course in Computational Algebraic Number Theory', Springer-Verlag Berlin Heidelberg New-York 1996, p. 383.

Links

• MathOverflow, Why are powers of exp(Pi*sqrt(163)) almost integers?
• Eric Weisstein's World of Mathematics, Almost Integer
• Wikipedia, Heegner number

Crossrefs

Cf. A166528, A166529, A166531, A166532.

Programs

Mathematica

RealDigits[Exp[Pi Sqrt[163]]^4,10,120][[1]]  (* Harvey P. Dale, Apr 20 2011 *)

PARI

exp(4*Pi*sqrt(163)) \\ Charles R Greathouse IV, Nov 12 2014