A241033 Decimal expansion of 'c', a constant such that in N steps, the mean longest random walk duration records grow as c*N.

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

Offset: 0

Author

Jean-François Alcover, Apr 15 2014

Keywords

• nonn
• cons

Examples

			0.626507598767175449080634422596159044653245248...
		

Links

• Steven Finch, Excursion Durations, May 12, 2008. [Cached copy, with permission of the author]
• Satya N. Majumdar and Robert M. Ziff, Universal Record Statistics of Random Walks and Lévy Flights, arXiv:0806.0057 [cond-mat.stat-mech], 2008.

Crossrefs

Cf. A084945 (the analog constant for i.i.d. random variables).

Programs

Mathematica

2*NIntegrate[Log[1 + 1/(2*Sqrt[Pi])*Gamma[-1/2, x]], {x, 0, Infinity}, WorkingPrecision -> 105] // RealDigits[#, 10, 100]& // First