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A079403
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Let G[t] be the set of numbers between 2^{t-1} and 2^t-1, inclusive. There is a unique number a[t] in G[t] so that the denominator of the a[t]-th partial sum of the double harmonic series is divisible by smaller 2-powers than its neighbors.
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1
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3, 6, 13, 27, 54, 109, 219, 439, 879, 1759, 3518, 7037, 14075, 28151, 56303, 112606, 225212, 450424, 900848, 1801696, 3603393
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| The n-th partial sum of double harmonic series is defined to be sum_{1\le k<l\le n} 1/(kl).
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LINKS
| J. Zhao, Partial sums of multiple zeta value series II: finiteness of $p$-divisible sets.
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FORMULA
| a(n+1)-2*a(n) = (a(n+1) mod 2); a(n)=floor(c*2^n) where c= 1.718232...=3 /2 + sum(k>=2, (a(k+1)-2*a(k))/2^k ) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 24 2003
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EXAMPLE
| a(3)=6 because sum_{1\le k<l\le 6} 1/(kl)= 203/90, 4 does not divide 90, while 4 divides the denominators of both sum_{1\le k<l\le 5} 1/(kl)=15/8 and sum_{1\le k<l\le 7} 1/(kl)=469/180
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MAPLE
| sequ := proc(T) local A, i, n, t, psum, innersum; psum := 0; innersum := 0; A := {}; for t to T-1 do for n from 2^t to 2^(t+1)-1 do innersum := innersum+2^T/(n-1) mod 2^(2*T); psum := psum+2^T*innersum/n mod 2^(2*T); if psum mod 2^(2*T-t+1)=0 then A := A union {n}; end if; od; od; RETURN(A); end:
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CROSSREFS
| Cf. A079404.
Sequence in context: A123247 A112306 A033129 * A065830 A055143 A092539
Adjacent sequences: A079400 A079401 A079402 * A079404 A079405 A079406
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KEYWORD
| more,nonn
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AUTHOR
| Jianqiang Zhao (jqz(AT)math.upenn.edu), Jan 06 2003
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