[seqfan] Re: Sloane's Sequence A023052

Thu Jun 18 01:29:24 CEST 2009

Here are the results of my program for this problem.  Each line has three 
numbers, "a b c" where c is an a-digit number equal to the sum of the bth 
powers of its digits (in the entries for 0 and 1, the value of b is 
arbitrary).

If my program is working correctly, this list is complete up to 86 digits.  
Note that while it is sorted first by the value of a, then by the value of 
b, it is not sorted by the value of c (for given values of a and b, the 
numbers are listed in descending order of number of "9" digits, then by 
descending order of number of "8" digits, and so on); some rearrangement 
will be needed to put it into b-file form for whatever existing or new 
sequences need it (at least A023052, A046074, A003321).  It would be a 
good idea for someone to check that the list here is consistent with the 
previous results on the problem (is not missing any previously reported 
values and all the values listed are indeed solutions), as implementing 
the search efficiently is a bit fiddly.

I'll leave the program running overnight and see how far it gets.  If 
people want such computations for bases other than 10, I can readily run 
those as well.

1 1 0
1 1 1
1 1 2
1 1 3
1 1 4
1 1 5
1 1 6
1 1 7
1 1 8
1 1 9
3 3 407
3 3 371
3 3 370
3 3 153
4 4 9474
4 4 8208
4 4 1634
4 5 4151
4 5 4150
5 5 93084
5 5 92727
5 5 54748
6 5 194979
6 6 548834
7 7 9926315
7 7 9800817
7 7 4210818
7 7 1741725
8 7 14459929
8 8 88593477
8 8 24678051
8 8 24678050
9 9 912985153
9 9 534494836
9 9 472335975
9 9 146511208
10 10 4679307774
11 11 94204591914
11 11 82693916578
11 11 49388550606
11 11 44708635679
11 11 42678290603
11 11 40028394225
11 11 32164049651
11 11 32164049650
12 13 564240140138
14 14 28116440335967
15 17 233411150132317
16 16 4338281769391371
16 16 4338281769391370
17 17 35875699062250035
17 17 35641594208964132
17 17 21897142587612075
19 19 4929273885928088826
19 19 4498128791164624869
19 19 3289582984443187032
19 19 1517841543307505039
20 20 63105425988599693916
21 21 449177399146038697307
21 21 128468643043731391252
23 23 35452590104031691935943
23 23 28361281321319229463398
23 23 27907865009977052567814
23 23 27879694893054074471405
23 23 21887696841122916288858
24 24 239313664430041569350093
24 24 188451485447897896036875
24 24 174088005938065293023722
24 25 832662335985815242605071
24 25 832662335985815242605070
24 25 114735624485461118832514
25 25 4422095118095899619457938
25 25 3706907995955475988644381
25 25 3706907995955475988644380
25 25 1553242162893771850669378
25 25 1550475334214501539088894
25 27 7584178683470015004720746
26 27 77888878776432530886487094
27 27 177265453171792792366489765
27 27 174650464499531377631639254
27 27 128851796696487777842012787
27 27 121270696006801314328439376
27 27 121204998563613372405438066
27 29 477144170826130800418527003
28 29 5022908050052864745436221003
28 29 4716716265341543230394614213
29 29 23866716435523975980390369295
29 29 19008174136254279995012734741
29 29 19008174136254279995012734740
29 29 14607640612971980372614873089
30 31 793545620525277858657607629822
31 31 2309092682616190307509695338915
31 31 1927890457142960697580636236639
31 31 1145037275765491025924292050346
32 32 17333509997782249308725103962772
32 33 32186410459473623435614002227248
33 33 186709961001538790100634132976991
33 33 186709961001538790100634132976990
34 34 1122763285329372541592822900204593
34 35 7673249664848285722449710136138169
34 35 5250083909873201044638631458484846
35 35 12679937780272278566303885594196922
35 35 12639369517103790328947807201478392
35 36 91097771122214850683543503173498149
36 37 618670315011216949642642321868915308
36 37 418510620208153136884574959404115822
37 37 1219167219625434121569735803609966019
37 38 7403697806790834730831423191927508283
37 38 7320233109580046612992702336326619665
38 38 12815792078366059955099770545296129367
38 39 83281830613691836766959173718984508549
38 39 83281823928125880164896079973522049472
38 39 16427762135335641330720936105651700735
39 39 115132219018763992565095597973971522401
39 39 115132219018763992565095597973971522400
41 42 36428594490313158783584452532870892261556
41 42 24202117350726607855379216981761437616685
42 43 865428295996489702819913290126290251086057
42 43 649929577038606483022256247961798702282298
42 43 541494183189741758024440515698931971170565
42 43 540133062379646837091926683197423034975342
42 43 431693315336650106841122671394059061346259
42 43 216196771535553659064432337763021725280303
42 43 110488001357745108347376522372211155920487
43 44 6810209536021751861114918348460992955509943
43 44 5856845793349592707882266933841781895916377
43 44 4870692736452280126562816349691961381966274
43 44 3906378741950401404540845367463938860869507
44 45 52629118994026288113690621458128419465866933
44 45 52455000909452690385913874112931520316143509
44 45 43988588628637966718625825202934800362393972
44 45 17804804411551074034314974935268388104718848
44 45 17674136814275371165896659566101835068144683
44 45 17500125632575295611741402478151097427104361
44 45 17500125632575295611741402478151097427104360
44 47 11176608005327184860540748325517113640156715
45 46 552652296628071929876997582254879810411842988
45 46 394500610649009608022685635958104085968134641
45 46 394500610649009608022685635958104085968134640
46 47 4959921468176469608573534993418650725564922822
46 47 3551561298137983224493440104432142398068825798
46 47 2844606761993812649569688176852543331764572068
46 47 2134869831132206002876377009473775323572880694
48 49 344121003015798953461109472522636869502957985402
50 51 55683645994157961689595909141165132491193429749749
50 51 27887539002613689375558346990932796323618371540363
52 53 3009336689622424785094591221547283824126694123199598
53 54 27051156903992754495077743355694541141634293209536961
53 54 27051156903992754495077743355694541141634293209536960
53 54 10185128017405712763334458116098808034687490694771371
53 54 10185128017405712763334458116098808034687490694771370
54 55 152490314755876303649798312407542072870728583784707998
54 55 152349829250452484527824009552907045495378563176436265
55 56 2193762240761908392137860899658607674401938496187046968
55 56 1644854105813017601539897250795638996670193545173003361
55 56 1644854105813017601539897250795638996670193545173003360
55 57 7425044555765382638854533483880098967904270880718551172
56 57 14799195103184806214749814246033579630671509034462600766
58 59 1199348308270467958191508402511086560689741786191274137702
58 59 1199348017964116555212449342061478333395100875934086835818
59 60 16177694250271739806081953963047779450935812520923227956595
59 60 14386811900482199401154446588646400893796400907674489355497
60 61 145594628412421292850519939876219279596702430926364267115105
60 61 129495102611459020639899678988620521527176986805703581773808
60 62 728475978403642829851741374904538477488655795900713421600735
61 63 9174852606662607726177801113678196820891166550496124294678699
61 63 9174068665920007399354696861478347413772775785696277538164169
61 63 9170144431794731395241531659460231665070329596345003191540766
61 63 6555596227062064149236682227581807831086975578631720991615578
62 63 11793324696943658158328433258762969319709773412597747795160016
63 64 129729706383218800940922971779520807379706064324417989786624799
63 65 955256077560898124111362540804498199913430761027746959651296683
63 65 636770469136417466364955567722746934055137198582293651605270191
63 65 636770469136417466364955567722746934055137198582293651605270190
63 65 318837185893346603188980535303806554143266328423752913750628227
64 66 2869032556128948648730781914863325788554564820004337576337232668
65 67 43000935886563968289752634109551097051201187416816241678263012587
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70 72 3553438751722209353785828652972982238018290915067701179641141744597606
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70 73 4576184254731358021508736680581233553038140183100454588503323862064927
71 73 41116572198679370141438775497217993049956318498620027248373806765892748
71 73 31982738898669210132895793141776842508096541353761882152276694866774666
72 74 205582861042633905876121455640752077295129372644698554631567376179510118
73 75 3700316223969295190898056273575265497669320144827046421899889375830405483
73 75 1480493151133336923757850588866842657640719395284151731112043686858505135
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74 76 19981103645368126063530673405116111466239230004128132443233693536490496580
75 77 329676995241259219652290644781990074114050658304476278485551197823404990655
75 77 299725182082914829020593000524819542453610289615490854258138278439745817926
75 77 209828332838903296785425072085620849064348618509574430652375622586089881962
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77 79 16995111457550831280171147958830535098578358324475309142189782311681388024129
79 81 1376488299602043798046604995801166573707947372610050906530476027518262410785085
80 83 47793038108743375555186236842719503355185573254039434633586220032828844823848882
81 83 191126920872036543599990805037229647326022895390239696168625044691834113847664243
82 84 1146801329013164489392520090533722248637878390975412163715983880319660165678513082
82 85 7740883644871794477646364058227912729460623650549579586025073438456461819410580176
82 85 6450871460021138988345572823866004248159777331467627225806211430559106484005920961
82 85 6450871460021138988345572823866004248159777331467627225806211430559106484005920960
83 85 11611267564790786969534556020052569823893335824504599653287217280978886725421808449
83 85 11611093878700807521863745322326039143695779961208573941316709607456134088705946891
83 85 11611093878700807521863745322326039143695779961208573941316709607456134088705946890
83 86 69667952784088639691808710701185383514870536392736044560367260582163761703295320272
84 87 627018522286470891882632668681027543419600149639882058602240723968908403034645431236
85 87 1044986406326311528991636347987244369771861372251854339940098138332469445418790741311
85 87 1044986406326311528991636347987244369771861372251854339940098138332469445418790741310
86 89 84643632116708195922987645239891163477663611188406349121604733508395128506269995104866
86 89 84643394974509418090811371449561914498145271503251035419414468072170408413858249954025
86 89 76178533769946464174319084662198481980526553009035236443395403973563460763055574296327
86 89 59250471357847603601785913244477520671839394130285071348736373963402777724938296116147
86 89 50786795847920598461348040551706207525330736215584268030397531059564837546391014340148

-- 
Joseph S. Myers
jsm at polyomino.org.uk