A143300 -id:A143300 - cp's OEIS frontend

A244293 Decimal expansion of 3/2 - gamma / log(2), a coin tossing constant related to the asymptotic evaluation of the expected length of the longest run of consecutive heads.

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

Offset: 0

Jean-François Alcover, Jun 25 2014

			0.66725382272313284935358248...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.11 Feller Coin Tossing Constants, p. 340.

G. C. Greubel, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Run.

Cf. A086253, A086254, A143300 (gamma/log(2)).

SetDefaultRealField(RealField(100)); R:=RealField(); 3/2 - EulerGamma(R)/Log(2); // G. C. Greubel, Oct 13 2018

RealDigits[3/2 - EulerGamma/Log[2], 10, 102] // First

default(realprecision, 100); 3/2 - Euler/log(2) \\ G. C. Greubel, Oct 13 2018

Expected length ~ log(n)/log(2) - (3/2-gamma/log(2)).

A244292 Decimal expansion of B, a constant related to the Goh-Schmutz constant and the asymptotic expected order of a random permutation.

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, Jun 25 2014

			B = 2.99047039937190479877827516942...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4.1 Symmetric Group, p. 287.

Eric Weisstein's MathWorld, Goh-Schmutz Constant

Cf. A143300.

b = NIntegrate[Log[1 + t]/(E^t - 1), {t, 0, Infinity}, WorkingPrecision -> 100]; B = 2*Sqrt[2*b]; RealDigits[B] // First

B = 2*sqrt(2*b), with b = A143300 = Goh-Schmutz constant = integral_(0..infinity) log(1 + t)/(e^t - 1) dt = 1.11786...

cp's OEIS Frontend

A244293 Decimal expansion of 3/2 - gamma / log(2), a coin tossing constant related to the asymptotic evaluation of the expected length of the longest run of consecutive heads.

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