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Search: id:A077155
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| A077155 |
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Let p(2n+1,x)=(x+1)(x+2)...(x+2n)(x+2n+1), a(n) is the smallest integer >0 such that p(2n+1,x)-k has only one real root for any k >=a(n). |
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+0
1
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| 1, 4, 96, 4930, 416615, 52346851, 9150486666, 2122773858331, 630854176216923, 233667907156182198, 105531126177212999940, 57078667671269237092154, 36423221938771375213756343, 27076505528935399371748578683
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) is the smallest integer strictly greater than the maximum value of p(2n+1,x) in the interval [ -1,-(2n+1)]. Note that this maximum value is attained by p(2n+1,x) at some root of its derivative. [From Max Alekseyev (maxale(AT)gmail.com), Oct 18 2008]
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PROGRAM
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(PARI) { a(n) = local(p, r, m); p=prod(k=1, 2*n+1, x+k); r=real(polroots(deriv(p))); m=vecmax(vector(#r, j, floor(subst(p, x, r[j])))); if( polsturm(p-m)<=1 || polsturm(p-m-1)>1, error("increase realprecision"); ); m+1 } [From Max Alekseyev (maxale(AT)gmail.com), Oct 18 2008]
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CROSSREFS
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Sequence in context: A068114 A089639 A062779 this_sequence A013042 A065140 A007106
Adjacent sequences: A077152 A077153 A077154 this_sequence A077156 A077157 A077158
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 29 2002
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EXTENSIONS
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a(5)..a(13) from Max Alekseyev (maxale(AT)gmail.com), Oct 18 2008
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