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A073011
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Decimal expansion of Salem constant.
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4
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1, 1, 7, 6, 2, 8, 0, 8, 1, 8, 2, 5, 9, 9, 1, 7, 5, 0, 6, 5, 4, 4, 0, 7, 0, 3, 3, 8, 4, 7, 4, 0, 3, 5, 0, 5, 0, 6, 9, 3, 4, 1, 5, 8, 0, 6, 5, 6, 4, 6, 9, 5, 2, 5, 9, 8, 3, 0, 1, 0, 6, 3, 4, 7, 0, 2, 9, 6, 8, 8, 3, 7, 6, 5, 4, 8, 5, 4, 9, 9, 6, 2, 0, 9, 6, 8, 3, 0, 1, 1, 5, 5, 8, 1, 8, 1, 5, 3, 9, 4, 6, 5, 9, 2, 0
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| This number is algebraic of degree 10.
The Salem constant given here is the smallest known value of Mahler's measure M(f)=abs(a_d)*Product_{k=1..d}max(1,abs(b_k)) of a polynomial f(x)=sum_{k=0..d}(a_k*x^k)=a_d*Product_{k=1..d}(x-b_k). The minimum occurs for Lehmer's polynomial (coefficients A070178) L(x)=x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1 with M(L)=1.1762808... - Hugo Pfoertner (hugo(AT)pfoertner.org), Mar 12 2006
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REFERENCES
| David Boyd, Small Salem numbers, Duke Math. Journal, vol. 44, 1977, pp. 315-328.
D. H. Lehmer, Factorization of certain cyclotomic functions, Annals of Math. vol. 34, 1933, pp. 461-479.
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LINKS
| Simon Plouffe, Salem Constant
Michael Mossinghoff, Lehmer's Problem.
Michael Mossinghoff, Small Salem Numbers.
Eric Weisstein's World of Mathematics, Salem Constants.
Eric Weisstein's World of Mathematics, Polylogarithm
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EXAMPLE
| 1.17628081825991750654407033847403505069341580656469...
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MATHEMATICA
| RealDigits[x/.FindRoot[x^10+x^9-Total[x^Range[3, 7]]+x+1==0, {x, 1, 2}, WorkingPrecision->120]][[1]] (* From Harvey P. Dale, Sep 08 2011 *)
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PROG
| (PARI) default(realprecision, 250); L(x)=x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1; solve(x=1.1, 1.2, L(x))
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CROSSREFS
| Cf. A070178 [Coefficients of Lehmer's polynomial].
Sequence in context: A011102 A068469 A181152 * A086312 A030797 A019908
Adjacent sequences: A073008 A073009 A073010 * A073012 A073013 A073014
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KEYWORD
| cons,nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 03 2002
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