# [seqfan] Re: A093893 Subsequence

Hagen von EItzen math at von-eitzen.de
Mon Jun 1 11:50:15 CEST 2009

```>
> On Fri, May 29, 2009 at 6:14 PM, Hagen von EItzen <math at
> von-eitzen.de <http://list.seqfan.eu/cgi-bin/mailman/listinfo/seqfan>>
> wrote:
>
> >/ //////a(12) <= 231111////////////
> />/ a(13) = //////231112 = 23205949656945057666311162427422570380321,
> />/ //////a(14) <= //////231113,
> />/ //////a(15) <= 9240114 ~ 3.3*1069; if of the form////// p4*q2,
> then p>104 or q>104.
> />/ //////a(16) = //////???, //////
> /
> Update:
>
> exact value:
> a(12) = 2113 * 14712 = 20326973048971
>

No, a(12) = 2112 * 421 * 1051 = 19699251391 -- and in that case I
*really* checked all smaller numbers,
i.e. all forms p^11, p^5*q, p^3*q^2, p^2*q*r, the latter taking most
time to verify.

> upper bounds:
> a(14) <= 23116 * 50821 = 7741816606631194948471381
> a(15) <= 1201214 * 1501512 = 4693882500443399337067739425681
> a(16) <= 120121 * 150151 * 180181 * 270271 = 878325738218239130821
> a(18) <= 40840812 * 51051012 * 8168161 =
> 3550762793626881654061078595276521
> a(19) <= 408408118
>
> For exact value of a(14), if it is not 7741816606631194948471381, then
> a(14) = p6*q where prime p<1400 and prime q>106.
>
In addition to this, I have: If a(14) is not ..., then p <= 1571 and
a(14) > 592195652118678643207 (and counting)

Hagen

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