[seqfan] Re: Next perfect power number?

[Zak Seidov]

 Anyone wish/can check/extend my results
(if not old/known/trivial.. etc)?
Thx

 Small differences d (up to 100) between consecutive ppn's n and m:
 n,m,d
1,4,3,
4,8,4,
8,9,1,
9,16,7,
16,25,9,
25,27,2,
27,32,5,
32,36,4,
36,49,13,
49,64,15,
64,81,17,
81,100,19,
100,121,21,
121,125,4,
125,128,3,
128,144,16,
144,169,25,
169,196,27,
196,216,20,
216,225,9,
225,243,18,
243,256,13,
256,289,33,
289,324,35,
324,343,19,
343,361,18,
361,400,39,
400,441,41,
441,484,43,
484,512,28,
512,529,17,
529,576,47,
576,625,49,
625,676,51,
676,729,53,
729,784,55,
784,841,57,
841,900,59,
900,961,61,
961,1000,39,
1000,1024,24,
1024,1089,65,
1089,1156,67,
1156,1225,69,
1225,1296,71,
1296,1331,35,
1331,1369,38,
1369,1444,75,
1444,1521,77,
1521,1600,79,
1600,1681,81,
1681,1728,47,
1728,1764,36,
1764,1849,85,
1849,1936,87,
1936,2025,89,
2025,2048,23,
2048,2116,68,
2116,2187,71,
2187,2197,10,
2197,2209,12,
2209,2304,95,
2304,2401,97,
2401,2500,99,
2704,2744,40,
2744,2809,65,
3025,3125,100,
3125,3136,11,
3364,3375,11,
4900,4913,13,
5776,5832,56,
5832,5929,97,
6859,6889,30,
7744,7776,32,
7921,8000,79,
8000,8100,100,
8100,8192,92,
8192,8281,89,
9216,9261,45,
10609,10648,39,
12100,12167,67,
13824,13924,100,
16807,16900,93,
19600,19683,83,
21904,21952,48,
24336,24389,53,
32761,32768,7,
39204,39304,100,
42849,42875,26,
50625,50653,28,
64000,64009,9,
79507,79524,17,
85184,85264,80,
91125,91204,79,
97336,97344,8,
131044,131072,28,
140608,140625,17,
166375,166464,89,
175561,175616,55,
177147,177241,94,
250000,250047,47,
274576,274625,49,
279841,279936,95,
373248,373321,73,
970225,970299,74,
1030225,1030301,76,
1295029,1295044,15,
2515396,2515456,60,
3511808,3511876,68,
6436343,6436369,26,
14348907,14348944,37,
45118016,45118089,73,
183250369,183250432,63,
199176704,199176769,65,
503284356,503284375,19,
2535525316,2535525376,60,
{18821096000, 18821096100, 100}
{143384152904, 143384152921, 17}
{542939080312, 542939080336, 24}
........................................
No new terms up to n=10159886433172644