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A242430
Decimal expansion of the unforgeable pattern-free binary word constant, a constant mentioned in A003000.
3
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, 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, 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
OFFSET
0,1
COMMENTS
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.
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 369.
See more references and links in A003000, which is the main entry for this subject.
EXAMPLE
0.267786840217889112376671403584302552555...
MATHEMATICA
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
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved