# [seqfan] Re: A093893 Subsequence

Hagen von EItzen math at von-eitzen.de
Wed Jun 3 17:44:40 CEST 2009

```> >> 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.

Update: Meanwhile I can say that: If a(14) != 7741816606631194948471381
then a(14) > 2884960349615742355753 and a(14) = p^6*q with p < 1000.

Hagen

```