[seqfan] Re: Sloane's Sequence A023052

[Richard Mathar]

hh> From seqfan-bounces at list.seqfan.eu Wed Jun 17 18:32:19 2009
hh> From: Hans Havermann <pxp at rogers.com>
hh> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
hh> Date: Wed, 17 Jun 2009 12:06:35 -0400
hh> Cc: Yongwhan Lim <yongwhan at stanford.edu>
hh> Subject: [seqfan] Re: Sloane's Sequence A023052
hh> ...
hh> But let me get back to Harvey Heinz's "PDI". If we exclude from  
hh> A023052 ("powerful" numbers: yet another confusion) numbers where the  
hh> power is equal to the length of the number, what remains?
hh> 
hh>   1                                      4150 (+1)
hh>   2                                      4151 (+1)
hh>   3                                    194979 (-1)
hh>   4                                  14459929 (-1)
hh>   5                              564240140138 (+1)
hh>   6                           233411150132317 (+2)

This list is complete up to the 53rd entry in A023052. The b-file
of A023052 (status=submitted) starts

1 0
2 1
3 2
4 3
5 4
6 5
7 6
8 7
9 8
10 9
11 153
12 370
13 371
14 407
15 1634
16 4150
17 4151
18 8208
19 9474
20 54748
21 92727
22 93084
23 194979
24 548834
25 1741725
26 4210818
27 9800817
28 9926315
29 14459929
30 24678050
31 24678051
32 88593477
33 146511208
34 472335975
35 534494836
36 912985153
37 4679307774
38 32164049650
39 32164049651
40 40028394225
41 42678290603
42 44708635679
43 49388550606
44 82693916578
45 94204591914
46 564240140138
47 28116440335967
48 233411150132317
49 4338281769391370
50 4338281769391371
51 21897142587612075
52 35641594208964132
53 35875699062250035

hh>   7                  114735624485461118832514 (+1)
hh>   8                  832662335985815242605070 (+1)
hh>   9                  832662335985815242605071 (+1)
hh> 10                 7584178683470015004720746 (+2)
hh> 11                77888878776432530886487094 (+1)
hh> 12               477144170826130800418527003 (+2)
hh> 13              4716716265341543230394614213 (+1)
hh> 14              5022908050052864745436221003 (+1)
hh> 15            793545620525277858657607629822 (+1)
hh> 16          32186410459473623435614002227248 (+1)
hh> 17        5250083909873201044638631458484846 (+1)
hh> 18        7673249664848285722449710136138169 (+1)
hh> 19       91097771122214850683543503173498149 (+1)
hh> 20      418510620208153136884574959404115822 (+1)
hh> 21      618670315011216949642642321868915308 (+1)
hh> 22     7320233109580046612992702336326619665 (+1)
hh> 23     7403697806790834730831423191927508283 (+1)
hh> 24    16427762135335641330720936105651700735 (+1)
hh> 25    83281823928125880164896079973522049472 (+1)
hh> 26    83281830613691836766959173718984508549 (+1)
hh> 
hh> Finally, we have Lionel E. Deimel, Jr. and Michael T. Jones with their  
hh> 1982 discovery:
hh> 
hh> 27 36428594490313158783584452532870892261556 (+1)
hh> ...

One might guess  that the values missing in
http://bbs.emath.ac.cn/viewthread.php?action=printable&tid=1104

are only of the "underflow" sort (power less than digit count)
due to some monotonic search strategy of their C-program (which I'm not trying
to reverse-engineer).

Richard