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

[Harvey P. Dale]

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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