[seqfan] Re: Smallest k>1 such that k^n+n is prime

[Hugo Pfoertner]

n=18^2=324 seems to be a likely candidate for the next occurrence of no
solution, checking k<10^6.

On Mon, Apr 16, 2018 at 8:13 PM, Harvey P. Dale <hpd at hpdale.org> wrote:

> Hugo:
>         I now see that k must be greater than 1 (from the subject line,
> rather than the text), so please ignore my post.
>         Best,
>         Harvey
>
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Harvey
> P. Dale
> Sent: Monday, April 16, 2018 2:13 PM
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] Re: Smallest k>1 such that k^n+n is prime
>
> Hugo:
>         Doesn't k=1 work for n=4?
>         Best,
>         Harvey
>
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Hugo
> Pfoertner
> Sent: Monday, April 16, 2018 1:33 PM
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] Smallest k>1 such that k^n+n is prime
>
> SeqFans,
>
> usually I now refrain from inventing "is prime" sequences, but a friend
> asked me, for which n there are no solutions for k^n+n=prime. The values of
> n for which I could not find a matching k were n=4, 27, 64, next > 170. If
> we say, k=0 if no such k exist, what are the next expected positions where
> this happens?
>
> A corresponding sequence from n=1 through n=65 would be:
> 2, 3, 2, 0, 2, 175, 16, 3, 2, 539, 32, 221, 118, 417, 2, 85, 14, 133, 22,
> 81, 76, 115, 12, 55, 28, 15, 0, 2465, 110, 31, 232, 117, 230, 3, 12, 851,
> 4, 375, 2, 1599, 48, 5461, 46, 15, 218, 6815, 78, 7, 100, 993, 28, 901,
> 624, 13, 252, 183, 226, 43247, 104, 5063, 1348, 777, 1294, 0, 1806,
>
> Hugo Pfoertner
>
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