(In reply to
computer exploration may lead to ideas for a proof by Charlie)
... we want the closest positive, so we should seek only positives, and truncate the value of n for a given m, rather than round it. The minimum then would be the 26 from m=1, n=1:
10 for M=1 to 40
20 P33=33^M
30 N=int(log(P33)/log(7))
40 P7=7^N
50 print M,N,P33-P7
60 next
run
1 1 26
2 3 746
3 5 19130
4 7 362378
5 8 33370592
6 10 1008992720
7 12 28777155776
8 14 728185545392
9 16 13178553832352
10 17 1298948471277242
11 19 39143211328353674
12 21 1109343650869700954
13 23 27671606653367587370
14 25 475263062119835721722
15 26 50551465161217666237808
16 28 1517998664917818916957280
17 30 42734171357572184883961424
18 32 1049598210148805971764915008
19 34 16965898147007866727357408048
20 35 1966915495838014505395745647658
21 37 58847112286403842171136124357626
22 39 1644960850715045602808241485062346
23 41 39731009191518726639548688688831130
24 43 598041058098306844702065991138339178
25 44 76514528693030837452010296279164833792
26 46 2280392236758936416816096804904010292720
27 48 63268170517601922019019288918719307761376
28 50 1500595735604157419567953157805198593104592
29 52 20744218592578600499817968758457163984431552
30 53 2975803677887896891288230122914819682432332442
31 55 88331545216251599551859495547142813891576116074
32 57 2431312160587901890039410526112447312616159959354
33 59 56535488553529118507874858841490749571846536975370
34 61 704478297718750361452011604278414160391085377704922
35 62 115707762479330214416554634913891070615488900984414608
36 64 3420067022998032357333707405199067592921545065014257280
37 66 93346043956761696589795162570561681434321142439370675824
38 68 2124127228266640798554598456579165579860195309900341395808
39 70 23237879639780882095778295562893338669238728087365611648848
40 71 4497943669969348400586363738848928041326890004103462917032458
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Posted by Charlie
on 2011-11-06 12:05:50 |
actually...
