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

[Richard Guy]

I make the next term to be
61+62^8  =  218340105584957   R.

On Wed, 31 Mar 2004, Pfoertner, Hugo wrote:

> -----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
> 
> 




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