A127583 Decimal expansion of smallest univoque Pisot Number.

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

Offset

1,2

Comments

The 2nd and 3rd smallest univoque Pisot numbers are 1.8866814375493413002581625771460337570154853175085... (A374750) and 1.9051661677540189095727878303640157935069696492981... (A374751).

Links

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

J.-P. Allouche, C. Frougny, K. G. Hare, On univoque Pisot numbers, arXiv:math/0610681 [math.NT], (23-October-2006)

J.-P. Allouche, C. Frougny, K. G. Hare, On univoque Pisot numbers, Math. Comp. 76 (2007), 1639-1660.

D. Terr and Eric Weisstein's World of Mathematics, Pisot Numbers.

Index entries for algebraic numbers, degree 14.

Formula

The largest real root of x^14 - 2*x^13 + x^11 - x^10 - x^7 + x^6 - x^4 + x^3 - x + 1. - Robert G. Wilson v, Jul 17 2007 (corrected, Joerg Arndt, Jun 13 2015)

Example

1.88000047865555118281806896989947911064560839482260578509980692092...

Mathematica

First@ RealDigits[ FindRoot[ x^14 - 2 x^13 + x^11 - x^10 - x^7 + x^6 - x^4 + x^3 - x + 1, {x, 1.88}, WorkingPrecision -> 111][[1, 2]]] (* Robert G. Wilson v, Jul 17 2007 *)
RealDigits[Root[x^14-2x^13+x^11-x^10-x^7+x^6-x^4+x^3-x+1, 2], 10, 120][[1]] (* Harvey P. Dale, Jan 18 2024 *)

Crossrefs

Cf. A374750, A374751.

Sequence in context: A392000 A197623 A291692 * A273818 A375369 A326801

Adjacent sequences: A127580 A127581 A127582 * A127584 A127585 A127586

Keyword

cons,nonn

Author

R. J. Mathar, Jun 13 2007

Extensions

More terms from Robert G. Wilson v, Jul 17 2007

Status

approved