A239049 Decimal expansion of Pi*(2/3)^(1/2).

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

Offset: 1

Author

Omar E. Pol, Mar 16 2014

Keywords

• nonn
• cons

Comments

Decimal expansion of Pi*6^(1/2)/3.

Constant found in the Hardy-Ramanujan asymptotic formula of the number of partitions of n, for n = 1.

Also constant mentioned in the DeSalvo-Pak paper, see pages 2, 4, 6.

Examples

			2.5650996603237281910880727193420128229345213351281846...
		

References

• G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, Cambridge, University Press, 1940, p. 117.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• S. DeSalvo and I. Pak, Log-concavity of the partition function, arXiv:1310.7982v1 [math.CO], 2013-2014.
• Steven Finch, Integer Partitions, Sep 22 2004. [Cached copy, with permission of the author]
• Index entries for transcendental numbers

Crossrefs

Cf. A000796.

Programs

Magma

R:=RealField(); Pi(R)*Sqrt(2/3); // G. C. Greubel, Mar 31 2018

Maple

evalf(Pi*(2/3)^(1/2), 120) # Vaclav Kotesovec, Oct 17 2014

Mathematica

RealDigits[Pi*Sqrt[2/3], 10, 100][[1]] (* G. C. Greubel, Mar 31 2018 *)

PARI

Pi*sqrt(2/3) \\ G. C. Greubel, Mar 31 2018

Formula

Equals A000796 * A157697.

Extensions

More terms from Vaclav Kotesovec, Oct 17 2014