The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A079403 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A079403

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.
(history; published version)

#21 by Bruno Berselli at Mon Jan 22 11:06:47 EST 2018

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proposed

approved

#20 by Michel Marcus at Mon Jan 22 10:59:53 EST 2018

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editing

proposed

#19 by Michel Marcus at Mon Jan 22 10:59:49 EST 2018

LINKS

J. Zhao, <a href="https://arxiv.org/abs/math/0303043">Partial sums of multiple zeta value series II: finiteness of p-divisible sets</a>, arXiv:math/0303043 [math.NT], 2003-2010. See (23) p. 11.

STATUS

approved

editing

#18 by Alois P. Heinz at Mon Jan 22 09:55:51 EST 2018

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proposed

approved

#17 by Michel Marcus at Mon Jan 22 09:53:54 EST 2018

STATUS

editing

proposed

#16 by Michel Marcus at Mon Jan 22 09:53:48 EST 2018

LINKS

J. Zhao, <a href="httphttps://arXivarxiv.org/abs/math.NT/0303043">Partial sums of multiple zeta value series II: finiteness of p-divisible sets</a>, arXiv:math/0303043 [math.NT], 2003-2010.

STATUS

proposed

editing

#15 by Jean-François Alcover at Mon Jan 22 09:34:21 EST 2018

STATUS

editing

proposed

#14 by Jean-François Alcover at Mon Jan 22 09:34:14 EST 2018

MATHEMATICA

nmax = 15; dhs = Array[HarmonicNumber[# - 1]/# &, 2^nmax] // Accumulate; Print["dhs finished"];

f[s_] := IntegerExponent[s // Denominator, 2];

a[2] = 3; a[n_] := a[n] = For[k = 2*a[n - 1], k <= 2^n - 1, k++, fk = f[dhs[[k]]]; If[f[dhs[[k-1]]] > fk && f[dhs[[k+1]]] > fk, Return[k]]];

Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 2, nmax}] (* Jean-François Alcover, Jan 22 2018 *)

STATUS

approved

editing

#13 by Joerg Arndt at Sun Nov 19 01:43:57 EST 2017

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proposed

approved

#12 by Jon E. Schoenfield at Sat Nov 18 21:32:51 EST 2017

STATUS

editing

proposed