m^j + (m+1)^k = prime

[Pfoertner, Hugo]

-----Ursprüngliche Nachricht-----
Von: Richard Guy [mailto:rkg at cpsc.ucalgary.ca]
Gesendet am: 30 March, 2004 00:13
An: Leroy Quet
Cc: seqfan at ext.jussieu.fr
Betreff: Re: m^j + (m+1)^k = prime

I get the next few terms to be

2393, 29, 31, 83537, 307, 37, 419, 41, 43, 1013,
47, 601, 701, 53, 757, 615497, 59, 61, 1049537,

but, as usual, this is handwork, so checks
are needed.     R.

SeqFans, Richard, Leroy,

I checked your results with a little program and got

3 5 7 29 11 13 71 17 19 131 23 157 2393 29 31 83537 307 37 419 41 43 1013
47 601 701 53 757 615497 59 61 1049537 2113 67 1259 71 73 1481 1483 79 1721
83 3613 1979 89 2161 4977017 2351 97 2549 101 103 2861 107 109 3191 113
3307 3539 3541 7321

 m  j  k     prime
 1  1  1         3
 2  1  1         5
 3  1  1         7
 4  1  2        29
 5  1  1        11
 6  1  1        13
 7  1  2        71
 8  1  1        17
 9  1  1        19
10  1  2       131
11  1  1        23
12  2  1       157
13  3  2      2393
14  1  1        29
15  1  1        31
16  1  4     83537
17  2  1       307
18  1  1        37
19  1  2       419
20  1  1        41
21  1  1        43
22  2  2      1013
23  1  1        47
24  2  1       601
25  1  2       701
26  1  1        53
27  2  1       757
28  4  2    615497
29  1  1        59
30  1  1        61
31  2  4   1049537
32  2  2      2113
33  1  1        67
34  1  2      1259
35  1  1        71
36  1  1        73
37  1  2      1481
38  2  1      1483
39  1  1        79
40  1  2      1721
41  1  1        83
42  2  2      3613
43  1  2      1979
44  1  1        89
45  1  2      2161
46  3  4   4977017
47  1  2      2351
48  1  1        97
49  1  2      2549
50  1  1       101
51  1  1       103
52  1  2      2861
53  1  1       107
54  1  1       109
55  1  2      3191
56  1  1       113
57  2  1      3307
58  1  2      3539
59  2  1      3541
60  2  2      7321
next term m=61 will have j or k >= 6.

Hugo