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 A073011 Decimal expansion of Lehmer's constant (also known as the Salem constant). 18
 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; text; internal format)
 OFFSET 1,3 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, Mar 12 2006 The Salem numbers were named after the Greek mathematician Raphaël Salem (1898-1963). - Amiram Eldar, May 01 2021 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. 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. EXAMPLE 1.17628081825991750654407033847403505069341580656469... 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 *) 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)) (PARI) polrootsreal(Pol([1, 1, 0, -1, -1, -1, -1, -1, 0, 1, 1]))[2] \\ Charles R Greathouse IV, Sep 03 2014 CROSSREFS Cf. A070178 (Coefficients of Lehmer's polynomial). Sequence in context: A276459 A181152 A244920 * A086312 A214280 A291081 Adjacent sequences: A073008 A073009 A073010 * A073012 A073013 A073014 KEYWORD cons,nonn AUTHOR Robert G. Wilson v, Aug 03 2002 EXTENSIONS Edited by N. J. A. Sloane, May 01 2012 STATUS approved

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Last modified March 31 10:52 EDT 2023. Contains 361646 sequences. (Running on oeis4.)