Numbers whose squares start with 4 identical digits, with 5, with 6...

[Hans Havermann]

J.H., seqfans:

> %C A094783 Why is 720 not in the sequence?? The divisors of 360 begin
>            1,2,3,4,5,6,8,9,10,12,15,18 and the divisors of 720 begin
>            1,2,3,4,5,6,8,9,10,12,15,16. - jhbubby(AT)mindspring.com,
>            Aug 23 2007

    720 is precluded by 420. (1,2,3,4,5,6,7,10,12,14,15,20,21,...)

-- 
Don Reble  djr at nk.ca


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>> So OEIS does not yet have the sequnce where a(n) is the smallest
>> integer whose n-th power begins with n identical digits, base 10?

Just to extend the result of my previous message... Here are 100  
terms of the smallest number whose nth power begins with *precisely*  
n identical digits (base ten):

42956198981667894338629574454339952067227726540914891801976397967042
291360898665726391428371108476861204315022935437135799517106000726097
402674480392899138714483164792918159253774753063425540009418402155161
2044107005489263539065778979357772203957990136333194085741463357277296
35393936831960575302634947362729425625618179817436412387164050537871235
338393612937547690466219581073753417142839471027090626489102150497857995
699686938646504146147814290693129515466931078584899403236978120410143306 
9
407314339726024029772701947585129735328816205577446136518459262266970177 
02
854857125580480549321024532748248174570075739435843061910450750234587520 
898
119652582873207178753563530548977175746401271027205373471340169156113116 
97391
406693916621106232984204404991140972101550845659063546340660088360216396 
59101
925582279760866056082648645771552766125762780032834721674147600991529037 
53812
325890701146406355607848106042669001695557946353649013268529468248991545 
2959933
445072336780747789403013641354216758593431591237164738716774988712024941 
29628167
217354434857259787111144685309716478495137601309713091911882576531161919 
551763601
514511005158438916683415624376284957659393511702961245831060665737993145 
0195697502
929852657771780612063697415087838041535831660917113840007422268576210984 
21850839761
238236835467663670956352515130893643524622903472390653639019375045601821 
411216969876
264628773412771773391405057499965851667823880936953895022534098705261979 
71765074497959
462000695349815341268273161920091221625716444880499491437895812377787065 
600171364718693
750792579304069571548949091595085715119576180862111993750407784251679556 
862227068648668
117845287143117294798873673806560834896071756230414809248799336054561260 
641688530008542
273644376485884509906309575017322572307589369884527297267425366244681764 
875442981116064231
178724930607003068898156904800113851796016387959045687231801708908100698 
2614670789926049706
145727274436153319905419313851215056024486429630722305465770407879174173 
84279915467319874239
148420190141679626859515951516933231483452398377886273552312213032292828 
398649860400565544876
112887879062407283009276924196494545775661136899297033925728958987860664 
0743987287034854542785
145059151044402769103878738268198637281571208268152259149561221442804281 
09655092663411849861152
862314553880459745306204755565534970294973173022420754614327977499387980 
53603558095437589669104
789548737082879547986199504451801831365221532819300917328660870348178543 
182339193127195621831685
270464379694613856091726842230144804211782682268571278448933718798980864 
76774560929223682825225723
955564873360930022985658583584545698782102154914286148002225299252802561 
53353081384414941642556479
100  
183428947812303310621509034159760570392100963004638723372398764326683885 
3933635421787232134841207026


For the less stringent condition of the nth power beginning with *at  
least* n identical digits, replace the numbers at indices  
{14,23,27,49,53} with:


Hans