# [seqfan] Re: A093893 Subsequence

Max Alekseyev maxale at gmail.com
Mon Jun 1 14:42:25 CEST 2009

```On Mon, Jun 1, 2009 at 5:50 AM, Hagen von EItzen <math at von-eitzen.de> wrote:

>> 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.

It's my fault -  somehow I've overlooked this solution. ;(

>> upper bounds:
>> a(14) <= 2311^6 * 50821 = 7741816606631194948471381
>> a(15) <= 120121^4 * 150151^2 = 4693882500443399337067739425681
>> a(16) <= 120121 * 150151 * 180181 * 270271 = 878325738218239130821
>> a(18) <= 4084081^2 * 5105101^2 * 8168161 =
>> 3550762793626881654061078595276521
>> a(19) <= 4084081^18
>>
>> For exact value of a(14), if it is not 7741816606631194948471381, then
>> a(14) = p6*q where prime p<1400 and prime q>10^6.
>>
> In addition to this, I have: If a(14) is not ..., then p <= 1571 and
> a(14) > 592195652118678643207 (and counting)

Nice. But please notice that 1571 is larger than 1400 in my bounds.
I've eliminated all larger primes p by brute-forcing q in the interval
up to
7741816606631194948471381 / nextprime(1400)^6 < 10^6.

Maximilian Hasler has also found the exact value of a(19):

a(19) =  2312311 ^18
=3571349994602512630844440515395987609584252947287517917035677177078084203820579522539956202921089723227183031100881

Max

```