A242430 Decimal expansion of the unforgeable pattern-free binary word constant, a constant mentioned in A003000.

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

Author

Jean-François Alcover, May 14 2014

Keywords

• nonn
• cons

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.

Examples

			0.267786840217889112376671403584302552555...
		

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.

Crossrefs

Cf. A003000, A006156, A007777, A028445, A045690.

Programs

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