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Search: id:A079404
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| A079404 |
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Let G(n) be the set of numbers between 2^{n-1} and 2^n-1, inclusive. There is a unique number m(n) in G(n) so that the denominator of the m(n)th partial sum of the double harmonic series is divisible by smaller 2-power than that of others in G(n). This power is defined to be a(n). |
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2
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| 0, 1, 3, 4, 3, 3, 5, 7, 9, 10, 9, 10, 12, 14, 13, 13, 15, 17, 19, 19
(list; graph; listen)
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OFFSET
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2,3
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COMMENT
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The sequence is conjectured to go to positive infinity.
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REFERENCES
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Partial sums of multiple zeta value series II: finiteness of $p$-divisible sets
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LINKS
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J. Zhao, Partial sums of multiple zeta value series II: finiteness of $p$-divisible sets.
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EXAMPLE
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a(2)=1 because G[2]={4,5,6,7} and among \sum{1\le k<l\le 4} 1/(kl)=35/24, \sum{1\le k<l\le 5} 1/(kl)=15/8, \sum{1\le k<l\le 6} 1/(kl)=203/90, \sum{1\le k<l\le 7} 1/(kl)=469/180, 90 has smallest 2-power factor among the denominators.
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MAPLE
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sequ := proc(T) local b, counter, A, n, t, psum, innersum; psum := 0; innersum := 0; A := array(1..T-1); for t to T-1 do for n from 2^(t) to 2^(t+1)-1 do innersum := innersum+1/(n-1); psum := psum+innersum/n; if 2^(2*t)*psum mod 2^(2*t+1)=0 then print(`The conjecture that 2 never divides the numerators of partial sums of double harmonic series is wrong.`); else b := 0; counter := 2*t; while b=0 do b := 2^counter*psum mod 2; counter := counter-1; od; if counter<t-1 then A[t] := counter+1: end if; end if; od; od; RETURN(eval(A)): end:
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CROSSREFS
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Cf. A079403.
Adjacent sequences: A079401 A079402 A079403 this_sequence A079405 A079406 A079407
Sequence in context: A092910 A073322 A006197 this_sequence A094237 A016654 A090673
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KEYWORD
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nonn
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AUTHOR
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Jianqiang Zhao (jqz(AT)math.upenn.edu), Jan 06 2003
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