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%I #4 May 15 2014 12:14:11
%S 2,6,7,7,8,6,8,4,0,2,1,7,8,8,9,1,1,2,3,7,6,6,7,1,4,0,3,5,8,4,3,0,2,5,
%T 5,2,5,5,5,0,5,9,8,9,7,9,9,3,4,8,4,5,3,2,0,7,6,3,1,1,8,8,8,5,1,1,2,1,
%U 4,9,3,7,7,8,5,2,3,2,7,6,2,8,5,3,5,4,4,7,6,2,2,3,8,5,6,1,3,6,8,4
%N Decimal expansion of the unforgeable pattern-free binary word constant, a constant mentioned in A003000.
%C A binary word (a word over a 2-letter alphabet) is said "unforgeable" if it never matches a left or right shift of itself. The limit lower bound of the number of unforgeable words of length n is (0.26778684...)*2^n.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 369.
%D See more references and links in A003000, which is the main entry for this subject.
%e 0.267786840217889112376671403584302552555...
%t digits = 100; k0 = 5; dk = 5; Clear[r]; r[k_] := r[k] = Sum[(-1)^(n-1)*2/(2^(2^(n+1)-1)-1) * Product[2^(2^m-1)/(2^(2^m-1)-1), {m, 2, n}], {n, 1, k}] // N[#, digits+10]&; r[k0]; r[k = k0 + dk]; While[RealDigits[r[k], 10, digits+10] != RealDigits[r[k - dk], 10, digits+10], Print["k = ", k]; k = k + dk]; RealDigits[r[k], 10, digits] // First
%Y Cf. A003000, A006156, A007777, A028445, A045690.
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, May 14 2014
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