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

[Pfoertner, Hugo]

SeqFans,

(sorry for the ~130 line posting)

I don't know if that is of any interest, but there are two other sequences
that can be constructed if we exclude the trivial case j=k=1:

3 7 13 29 31 43 71 73 109 131 14653 157 2393 211 241 83537 307 379
419 421 463 1013 599 601 701 19709 757 615497 929 991 1049537 2113
1123 1259 2521 51949 1481 1483 3121 1721 1723 3613 1979 2069 2161
4977017 2351 110641 2549 2551 140659 2861 2969 2971 3191 175673
3307 3539 3541 7321

 1  2  1         3
 2  2  1         7
 3  2  1        13
 4  1  2        29
 5  2  1        31
 6  2  1        43
 7  1  2        71
 8  2  1        73
 9  1  2       109
10  1  2       131
11  4  1     14653
12  2  1       157
13  3  2      2393
14  2  1       211
15  2  1       241
16  1  4     83537
17  2  1       307
18  1  2       379
19  1  2       419
20  2  1       421
21  2  1       463
22  2  2      1013
23  1  2       599
24  2  1       601
25  1  2       701
26  1  3     19709
27  2  1       757
28  4  2    615497
29  1  2       929
30  1  2       991
31  2  4   1049537
32  2  2      2113
33  2  1      1123
34  1  2      1259
35  2  2      2521
36  2  3     51949
37  1  2      1481
38  2  1      1483
39  2  2      3121
40  1  2      1721
41  2  1      1723
42  2  2      3613
43  1  2      1979
44  1  2      2069
45  1  2      2161
46  3  4   4977017
47  1  2      2351
48  3  1    110641
49  1  2      2549
50  2  1      2551
51  1  3    140659
52  1  2      2861
53  1  2      2969
54  2  1      2971
55  1  2      3191
56  3  1    175673
57  2  1      3307
58  1  2      3539
59  2  1      3541
60  2  2      7321

or if we require min(j,k)>1:

5 13 43 41 61 379 113 593 181 14741 16369 313 2393 421 3631 83777
613 105337 761 9661 205129 1013 12743 1201 1301 20359 1146097 615497
1741 1861 1049537 2113 2522257 2381 2521 51949 3959297 56393 3121
2561681 115930289 3613 7166897 3839221 93241 4977017 4513 119953
6252401 5101 7314217

 1  2  2         5
 2  2  2        13
 3  3  2        43
 4  2  2        41
 5  2  2        61
 6  2  3       379
 7  2  2       113
 8  3  2       593
 9  2  2       181
10  2  4     14741
11  4  3     16369
12  2  2       313
13  3  2      2393
14  2  2       421
15  3  2      3631
16  2  4     83777
17  2  2       613
18  4  2    105337
19  2  2       761
20  2  3      9661
21  4  3    205129
22  2  2      1013
23  3  2     12743
24  2  2      1201
25  2  2      1301
26  2  3     20359
27  4  4   1146097
28  4  2    615497
29  2  2      1741
30  2  2      1861
31  2  4   1049537
32  2  2      2113
33  4  4   2522257
34  2  2      2381
35  2  2      2521
36  2  3     51949
37  4  4   3959297
38  3  2     56393
39  2  2      3121
40  4  2   2561681
41  5  3 115930289
42  2  2      3613
43  4  4   7166897
44  4  3   3839221
45  3  2     93241
46  3  4   4977017
47  2  2      4513
45  3  2     93241
46  3  4   4977017
47  2  2      4513
48  2  3    119953
49  2  4   6252401
50  2  2      5101

Hugo