Search: id:A073011
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%I A073011
%S A073011 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,
%T A073011 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,
%U A073011 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
%N A073011 Decimal expansion of Salem constant.
%C A073011 This number is algebraic of degree 10.
%C A073011 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
%D A073011 David Boyd, Small Salem numbers, Duke Math. Journal, vol. 44, 1977, pp. 
               315-328.
%D A073011 D. H. Lehmer, Factorization of certain cyclotomic functions, Annals of 
               Math. vol. 34, 1933, pp. 461-479.
%H A073011 Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/
               sci/math/MiscellaneousMathematicalConstants/chap81.html">Salem Constant</
               a>
%H A073011 Michael Mossinghoff, <a href="http://oldweb.cecm.sfu.ca/~mjm/Lehmer/">
               Lehmer's Problem.</a>
%H A073011 Michael Mossinghoff, <a href="http://www.cecm.sfu.ca/~mjm/Lehmer/lists/
               SalemList.html">Small Salem Numbers.</a>
%H A073011 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SalemConstants.html">Salem Constants.</a>
%H A073011 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Polylogarithm.html">Polylogarithm</a>
%e A073011 1.17628081825991750654407033847403505069341580656469...
%Y A073011 Cf. A070178 [Coefficients of Lehmer's polynomial].
%Y A073011 Sequence in context: A138096 A011102 A068469 this_sequence A086312 A030797 
               A019908
%Y A073011 Adjacent sequences: A073008 A073009 A073010 this_sequence A073012 A073013 
               A073014
%K A073011 cons,nonn
%O A073011 1,3
%A A073011 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 03 2002

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