# [seqfan] Re: Next perfect power number?

Zak Seidov zakseidov at mail.ru
Mon Jul 18 11:02:22 CEST 2016

``` Two examples of codes used by me:

(PARI) {a = 373248; for (k = 1, 10^8, s = []; for (i = 2, 13,
s = concat (s, (floor ((2 + a)^(1/i)) + 1)^i)); b = vecmin (s);
if (b - a < 101, print (a "," b "," b - a ",")); a = b)}

(MMa)   a = 373248; Do[b = Min[Table[(Floor[a^(1/i)] + 1)^i, {i, 2, 10}]];
If[b - a < 101, Print[{a, b, b - a}]]; a = b, {10^6}]

In all cases, PARI is (much more) faster than Mma.

>Понедельник, 18 июля 2016, 11:03 +03:00 от Zak Seidov via SeqFan <seqfan at list.seqfan.eu>:
>
>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
>
>
>
>--
>Seqfan Mailing list -  http://list.seqfan.eu/

```