A073011 Decimal expansion of Lehmer's constant (also known as the Salem constant).
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
Offset: 1
Examples
1.17628081825991750654407033847403505069341580656469...
References
- Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.30, p. 193.
Links
- G. C. Greubel, Table of n, a(n) for n = 1..5000
- David Boyd, Small Salem numbers, Duke Math. Journal, vol. 44, 1977, pp. 315-328.
- Henri Cohen, Leonard Lewin, and Don Zagier. A sixteenth-order polylogarithm ladder, Experimental Mathematics 1.1 (1992): 25-34.
- Eriko Hironaka, What is Lehmer's number?, Notices Amer. Math. Soc., 56 (No. 3, 2009), 374-375.
- D. H. Lehmer, Factorization of certain cyclotomic functions, Annals of Math. vol. 34, 1933, pp. 461-479.
- Douglas Lind, Lehmer's Problem for compact abelian groups, arXiv:math/0303279 [math.NT], 2003-2014.
- Michael Mossinghoff, Lehmer's Problem Website.
- Michael Mossinghoff, Small Salem Numbers.
- Simon Plouffe, Salem Constant.
- Raphaël Salem, Power series with integral coefficients, Duke mathematical journal, Vol. 12, No. 1 (1945), pp. 153-172.
- Eric Weisstein's World of Mathematics, Salem Constants.
- Eric Weisstein's World of Mathematics, Polylogarithm.
- Index entries for algebraic numbers, degree 10
Crossrefs
Cf. A070178 (Coefficients of Lehmer's polynomial).
Programs
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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]] (* Harvey P. Dale, Sep 08 2011 *) Root[ x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1, 2] // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Mar 05 2013 *)
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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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PARI
polrootsreal(Pol([1, 1, 0, -1, -1, -1, -1, -1, 0, 1, 1]))[2] \\ Charles R Greathouse IV, Sep 03 2014
Formula
This is the largest real root of the polynomial x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1.
Extensions
Edited by N. J. A. Sloane, May 01 2012
Comments