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A374752
Decimal expansion of phi_4, a limit point of the set of Pisot numbers in (1,2).
2
1, 9, 3, 3, 1, 8, 4, 9, 8, 1, 8, 9, 9, 5, 2, 0, 4, 4, 6, 7, 9, 1, 4, 2, 4, 0, 3, 0, 3, 3, 5, 6, 3, 1, 5, 8, 6, 3, 7, 5, 1, 8, 3, 7, 8, 4, 4, 7, 9, 2, 5, 4, 3, 9, 4, 0, 1, 8, 7, 6, 3, 7, 3, 0, 1, 8, 6, 3, 5, 2, 8, 5, 7, 3, 9, 9, 4, 7, 1, 2, 3, 5, 8, 0, 7, 5, 6, 7, 2, 5
OFFSET
1,2
LINKS
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).
Kevin G. Hare and Nikita Sidorov, Conjugates of Pisot numbers, International Journal of Number Theory, Vol. 17, No. 06 (2021), pp. 1307-1321 (arXiv version).
Eric Weisstein's World of Mathematics, Pisot Number.
FORMULA
Equals the real root of x^5 - 2*x^4 + x - 1.
Using the notation of Hare and Sidorov (2021, see Theorem 3.1), phi_1 = psi_1 (A001622) < phi_2 (A109134) < psi_2 (A058265) < phi_3 (A275828) < chi (A374751) < psi_3 (A086088) < phi_4 (this constant) < ... < psi_r < phi_(r+1) < ... < 2.
EXAMPLE
1.933184981899520446791424030335631586375183784479...
MATHEMATICA
First[RealDigits[Root[#^5 - 2*#^4 + # - 1 &, 1], 10, 100]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Paolo Xausa, Jul 18 2024
STATUS
approved