A245279 Decimal expansion of a1, the first of two constants associated with Djokovic's conjecture on an integral inequality.

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

Offset

0,2

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.1.1 Djokovic's Conjecture, p. 210.

Links

Table of n, a(n) for n=0..102.

Formula

Positive root of 12*x^3 - 16*x^2 + 8*x - 1.

Equals (r - 8/r + 8)/18, where r = (27*sqrt(17)-109)^(1/3).

Example

0.1824878875219793398416793914878206648753039383250540321198664994565...

Mathematica

a1 = Root[12*x^3 - 16*x^2 + 8*x - 1, x, 1]; RealDigits[a1, 10, 103] // First

Crossrefs

Cf. A245280.

Sequence in context: A073440 A245533 A021552 * A321071 A008830 A248302

Adjacent sequences: A245276 A245277 A245278 * A245280 A245281 A245282

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 16 2014

Status

approved