A374750 -id:A374750 - cp's OEIS frontend

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

R. J. Mathar, Jun 13 2007

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

			1.88000047865555118281806896989947911064560839482260578509980692092...

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.

Cf. A374750, A374751.

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 *)

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)

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

A374751 Decimal expansion of the third smallest univoque Pisot number.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jul 18 2024

This number is denoted by Allouche et al. (2007) as chi. It's the unique Pisot number of degree 4 which is univoque (see Remark 4.1, p. 1646), and the smallest limit point of univoque Pisot numbers (see Theorem 5.3, p. 1651).

			1.905166167754018909572787830364015793506969649298...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Jean-Paul Allouche, Christiane Frougny, and Kevin G. Hare, On Univoque Pisot Numbers, Mathematics of Computation, Vol. 76, No. 259, July 2007, pp. 1639-1660 (arXiv version).
Eric Weisstein's World of Mathematics, Pisot Number.
Wikipedia, Pisot-Vijayaraghavan number.
Index entries for algebraic numbers, degree 4.

Cf. A127583 (smallest), A374750 (second smallest), A374752.

First[RealDigits[Root[#^4 - #^3 - 2*#^2 + 1 &, 2], 10, 100]]

Equals the real root > 1 of x^4 - x^3 - 2*x^2 + 1.

cp's OEIS Frontend

A127583 Decimal expansion of smallest univoque Pisot Number.

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