A248852 Decimal expansion of a variant of the Komornik-Loreti constant.

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

Offset

1,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.8 Prouhet-Thue-Morse Constant, p. 438.

Links

Table of n, a(n) for n=1..102.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 56.

Eric Weisstein's MathWorld, Komornik-Loreti Constant

Formula

The number 'q' is the unique positive solution of Sum_{n >= 1} (1-t(n)-t(n-1))*q^-n = 1, where t(n) = A010060(n).

Example

2.5359480481498938851124689041808082087833552617...

Mathematica

RealDigits[ q /. FindRoot[ Sum[(1 + Mod[DigitCount[n, 2, 1], 2] - Mod[DigitCount[n - 1, 2, 1], 2])/q^n, {n, 1, 2000}] == 1, {q, 5/2}, WorkingPrecision -> 120], 10, 102] // First

Crossrefs

Cf. A010060, A055060, A248853.

Sequence in context: A368658 A216052 A021911 * A299210 A104978 A365723

Adjacent sequences: A248849 A248850 A248851 * A248853 A248854 A248855

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Mar 03 2015

Status

approved