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

Author

R. J. Mathar, Jun 13 2007

Keywords

• cons
• nonn
• changed

Comments

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

Examples

			1.88000047865555118281806896989947911064560839482260578509980692092...
		

Links

• 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.

Crossrefs

Cf. A374750, A374751.

Programs

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 *)

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)

Extensions

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