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Search: id:A014176
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| A014176 |
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Decimal expansion of the silver mean, 1+sqrt(2). |
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+0
13
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| 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, 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, 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
(list; cons; graph; listen)
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OFFSET
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1,1
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LINKS
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Eric Weisstein's World of Mathematics, Silver Ratio
Wikipedia, Silver ratio
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FORMULA
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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).
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.
1/c=sqrt(2)-1.
See A001622 for a general formula concerning the fractional parts of powers of numbers x>1, which suffice x-x^(-1)=floor(x).
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)
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CROSSREFS
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Cf. A002193.
Cf. A000032, A006497, A080039.
Adjacent sequences: A014173 A014174 A014175 this_sequence A014177 A014178 A014179
Sequence in context: A157284 A143973 A011167 this_sequence A060047 A135185 A011029
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KEYWORD
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nonn,cons
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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