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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 (list; constant; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..99.

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

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

Sequence in context: A061352 A173991 A039926 * A035569 A176017 A140132

Adjacent sequences:  A242427 A242428 A242429 * A242431 A242432 A242433

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, May 14 2014

STATUS

approved

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Last modified January 24 19:03 EST 2022. Contains 350565 sequences. (Running on oeis4.)