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

0,1

References

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Run.

Formula

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

Example

0.66725382272313284935358248...

Mathematica

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

Prog

(PARI) default(realprecision, 100); 3/2 - Euler/log(2) \\ G. C. Greubel, Oct 13 2018
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); 3/2 - EulerGamma(R)/Log(2); // G. C. Greubel, Oct 13 2018

Crossrefs

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

Sequence in context: A375657 A375640 A247253 * A196737 A070058 A160057

Adjacent sequences: A244290 A244291 A244292 * A244294 A244295 A244296

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 25 2014

Status

approved