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Search: id:A111000
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| A111000 |
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Integer part of Zeta(Zeta(n)). |
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+0
1
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| 2, 5, 12, 27, 58, 120, 245, 498, 1006, 2024, 4064, 8149, 16327, 32692, 65435, 130938, 261966, 524051, 1048260, 2096731, 4193743, 8387860, 16776219, 33553102, 67107091, 134215365, 268432305, 536866711, 1073736223, 2147476181
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Notice the previous term is almost 1/2 the next term. Conjecture: limit_{ n -> infinity } zeta(zeta(n))/zeta(zeta(n+1)) = 1/2.
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FORMULA
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Zeta(s) = Sum(1/n^s, n=1, 2, ..inf).
For n>=2, a(n)=floor(2^n-(4/3)^n-1+gamma+(8/9)^n-(4/5)^n+(2/3)^n) - Benoit Cloitre (abcloitre(AT)wanadoo.fr), Oct 04 2005
a(n)=2^n-(4/3)^n+O(1) and more precisely lim n-->infty zeta(zeta(n))-2^n+(4/3)^n+1=gamma where gamma is the Euler-Mascheroni constant. - Benoit Cloitre (abcloitre(AT)wanadoo.fr), Oct 04 2005
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EXAMPLE
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A(100) ~ 1267650600228229398378720795167.
A(101) ~ 2535301200456458798836096530474.
A(100)/A(101) ~ 0.49999999999999999959005759..
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PROGRAM
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(PARI) zz(n) = for(x=2, n, print1(floor(zeta(zeta(x)))", "))
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CROSSREFS
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Sequence in context: A128812 A078410 A096766 this_sequence A000325 A076878 A129983
Adjacent sequences: A110997 A110998 A110999 this_sequence A111001 A111002 A111003
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Sep 30 2005
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