A244046 Decimal expansion of the maximal width of a Reuleaux triangle avoiding all vertices of the integer square lattice.

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

Offset

1,2

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.10 Reuleaux triangle constants, p. 515.

Links

Table of n, a(n) for n=1..105.

Eric Weisstein's MathWorld, Reuleaux Triangle

Wikipedia, Reuleaux Triangle

Formula

Smallest positive root of 4*x^6 - 12*x^5 + x^4 + 22*x^3 - 14*x^2 - 4*x + 4.

Example

1.54494170037159315418509683847062658...

Mathematica

w = Root[4*x^6 - 12*x^5 + x^4 + 22*x^3 - 14*x^2 - 4*x + 4, x, 3]; RealDigits[w, 10, 105] // First

Crossrefs

Cf. A060708, A066666, A137615.

Sequence in context: A357418 A303270 A340918 * A255332 A071419 A291069

Adjacent sequences: A244043 A244044 A244045 * A244047 A244048 A244049

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 18 2014

Status

approved