[seqfan] Re: Searched further in A176245 Primes of the form A174881(k)-1 or A174881(k)+1

[Farideh Firoozbakht]

Dear Dr. Post,

There is no prime of the form A174881(k)-1. Because k(k+1)-1 divides
A174881(k)-1=(k(k+1))^k-1.
So I think definition of the sequence A176245 should be changed.

Also if A174881(k)+1 is prime then k must be of the form 2^n.

Between the first 14 such integers k, only for k = 2^0, 2^1 & 2^2
A174881(k)+1 is prime.
So next term of the sequence (if it exists) is greater than
((2^14)*(2^14+1))^(2^14). Namely it has more than 138099 digits.

Note that (40*(41))^8+1 divides ((40*(41+1))^40+1 and ((90*(90+1))^2+1
divides ((90*(90+1))^90+1, so both numbers ((40*(41+1))^40+1 and
((90*(90+1))^90+1 are composite.


Farideh


Quoting Jonathan Post <jvospost3 at gmail.com>:

> No more than the 3 prime values shown through ((90*(90+1))^90) + 1.
> Factorization gets slow for these, exceeding 200 digits.
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>









----------------------------------------------------------------
University of Isfahan (http://www.ui.ac.ir)