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Decimal expansion of C, a coin tossing constant related to the asymptotic variance of the length of the longest run of consecutive heads.
1

%I #13 Mar 07 2023 10:32:08

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

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

%U 8,5,5,0,3,2,5,7,0,7,2,8,9,8,5,7,3,8,7,2,5,1,8,8,2,3,7,9,4,1,2,2,3,2,0,4,1

%N Decimal expansion of C, a coin tossing constant related to the asymptotic variance of the length of the longest run of consecutive heads.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.11 Feller Coin Tossing Constants, p. 341.

%H Vincenzo Librandi, <a href="/A245673/b245673.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Run.html">Run</a>.

%F C = 1/12 + Pi^2/(6*log(2)^2).

%e 3.5070480758706367308268590108982890057364203565822690606175079937554855...

%t RealDigits[1/12 + Pi^2/(6*Log[2]^2), 10, 105] // First

%Y Cf. A244293.

%K nonn,cons,easy

%O 1,1

%A _Jean-François Alcover_, Jul 29 2014