A195202 Unique constant x that satisfies: x = Sum_{n>=1} 1/floor(x^n).

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

Offset

1,2

Links

Paul D. Hanna, Table of n, a(n) for n = 1..1971

Formula

x = Sum_{n>=1} 1/A066173(n) where floor(x^n) = A066173(n).

Example

Constant x = 1.7767914254 8765842099 7295125934 3751657100 4017014991 1002131974 4535225732 9321570657 9706460392 2109445017 4890160620 5702665489 ...
The integer floor of the powers of the constant x begin:
1=[x], 3=[x^2], 5=[x^3], 9=[x^4], 17=[x^5], 31=[x^6], 55=[x^7], 99=[x^8], 176=[x^9], 313=[x^10], ..., A066173(n) = [x^n], ...
where
x = 1/1 + 1/3 + 1/5 + 1/9 + 1/17 + 1/31 + 1/55 + 1/99 + 1/176 + 1/313 + 1/557 + 1/990 + 1/1759 + 1/3125 + 1/5553 + 1/9866 +...+ 1/[x^n] +...

Mathematica

digits = 100; Clear[s]; s[m_] := s[m] = x /. FindRoot[x == Sum[1/Floor[x^n], {n, 1, m}], {x, 2, 1, 2}, WorkingPrecision -> digits]; s[0] = 0; dm = 100; s[m = dm]; While[ RealDigits[s[m], 10, digits][[1]] != RealDigits[s[m - dm], 10, digits][[1]], m = m + dm; Print[m, " terms"]]; RealDigits[s[m], 10, digits] // First (* Jean-François Alcover, Jun 25 2013 *)

Crossrefs

Cf. A066173.

Sequence in context: A280507 A059965 A124930 * A252799 A022619 A131685

Adjacent sequences: A195199 A195200 A195201 * A195203 A195204 A195205

Keyword

nonn,cons

Author

Paul D. Hanna, Sep 12 2011

Status

approved