Search: id:A014176
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%I A014176
%S A014176 2,4,1,4,2,1,3,5,6,2,3,7,3,0,9,5,0,4,8,8,0,1,6,8,8,7,2,4,2,0,9,6,9,
%T A014176 8,0,7,8,5,6,9,6,7,1,8,7,5,3,7,6,9,4,8,0,7,3,1,7,6,6,7,9,7,3,7,9,9,
%U A014176 0,7,3,2,4,7,8,4,6,2,1,0,7,0,3,8,8,5,0,3,8,7,5,3,4,3,2,7,6,4,1,5,7
%N A014176 Decimal expansion of the silver mean, 1+sqrt(2).
%H A014176 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SilverRatio.html">Silver Ratio</a>
%H A014176 Wikipedia, <a href="http://en.wikipedia.org/wiki/silver_ratio">Silver 
               ratio</a>
%F A014176 Comments from Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jan 
               02 2009 (Start): Set c:=1+sqrt(2). Then the fractional part of c^n 
               equals 1/c^n, if n odd. For even n, the fractional part of c^n is 
               equal to 1-(1/c^n).
%F A014176 c:=1+sqrt(2) satisfies c-c^(-1)=floor(c)=2, hence c^n+(-c)^(-n)=nint(c^n) 
               for n>0, which follows from the general formula of A001622.
%F A014176 1/c=sqrt(2)-1.
%F A014176 See A001622 for a general formula concerning the fractional parts of 
               powers of numbers x>1, which suffice x-x^(-1)=floor(x).
%F A014176 Other examples of constants x satisfying the relation x-x^(-1)=floor(x) 
               include A001622 (the golden ratio: where floor(x)=1) and A098316 
               (the "bronze" ratio: where floor(x)=3). (End)
%Y A014176 Cf. A002193.
%Y A014176 Cf. A000032, A006497, A080039.
%Y A014176 Sequence in context: A157284 A143973 A011167 this_sequence A060047 A135185 
               A011029
%Y A014176 Adjacent sequences: A014173 A014174 A014175 this_sequence A014177 A014178 
               A014179
%K A014176 nonn,cons
%O A014176 1,1
%A A014176 N. J. A. Sloane (njas(AT)research.att.com).

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