[seqfan] Re: Question from Harvey Dale about A233552
Hugo Pfoertner
yae9911 at gmail.com
Tue May 28 12:43:06 CEST 2019
Just for clarification: 3145 is eliminated by (3145*4^39870-1)/3 being a
(pseudo)prime. Therefore in a sequence for replacement of A233552 the first
term with unknown status is at the moment 3991 (no primes through k=27000).
6019 and 8869 also lead to primes and may be dropped from the list of
numbers with unknown status.
On Tue, May 28, 2019 at 2:36 AM David Radcliffe <dradcliffe at gmail.com>
wrote:
> All of the terms listed in A233552 are correct, but many are missing. Here
> are the correct initial terms for A233552:
> 25, 49, 121, 169, 289, 361, 529, 625, 841, 919, 961, 1225, 1369, 1681,
> 1849, 2209, 2401, 2419, 2629, 2809, 3025
>
> All numbers of the form (6k + 1)^2 or (6k - 1)^2 with k >= 1 are terms.
>
> The following numbers are terms because they have covering sets of prime
> divisors:
> 919, 2419, 2629, 3301, 5209, 5539, 5581, 6421, 7771, 8551, 9109, 9871,
> 10039, 10819, 11491, 13399, 13729, 13771, 14611, 15661, 15961, 16741,
> 17299, 18061, 18229, 18799, 19009, 19681, 21589, 21919, 21961, 24151,
> 24931, 25489
>
> The covering set for 15661 is {3,5,7,17,241}. For the rest, {3,5,7,11,13}
> is a covering set, not necessarily minimal.
>
> The following numbers have unknown status. For each n in this list, I have
> not found k < 10000 such that (n*4^k-1)/3 is a pseudoprime, nor have I
> found a covering set.
>
> 3145, 3991, 5461, 6019, 7309, 8869, 12091, 14701, 18439, 19651, 20569,
> 21289, 21781, 22171, 22285, 22519, 22789, 22891
>
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