Seeking the largest "Small Brain Number". Upper and/or lower bounds?

Edit2:

All calculations for nothing.

Someone else did it before ^^

XXX http://oeis.org/A005188 XXX

115132219018763992565095597973971522401 , 39 digits.

n=1 : 1,2,3,4,5,6,7,8,9

n=3 : 153,370,371,407

n=4 : 1634,8208,9474

n=5 : 54748,92727,93084

n=6 : 548834

n=7 : 1741725,4210818,9800817,9926315

n=8 : 24678050,24678051,88593477

n=9 : 146511208,472335975,534494836,912985153

n=10: 4679307774

n=11: 32164049650,32164049651,

40028394225,42678290603,

44708635679,49388550606,

82693916578,94204591914

n=14: 28116440335967

n=16: 4338281769391370,4338281769391371

n=17: 21897142587612075,

35641594208964132,

35875699062250035

n=19: 1517841543307505039,

3289582984443187032,

4498128791164624869,

4929273885928088826

n=20: 63105425988599693916

n=21: 128468643043731391252,

449177399146038697307

n=23: 21887696841122916288858,

27879694893054074471405,

27907865009977052567814,

28361281321319229463398,

35452590104031691935943

n=24: 174088005938065293023722,

188451485447897896036875,

239313664430041569350093

n=25: 1550475334214501539088894,

1553242162893771850669378,

3706907995955475988644380,

3706907995955475988644381,

4422095118095899619457938

n=27: 121204998563613372405438066,

121270696006801314328439376,

128851796696487777842012787,

174650464499531377631639254,

177265453171792792366489765

n=29: 14607640612971980372614873089,

19008174136254279995012734740,

19008174136254279995012734741,

23866716435523975980390369295

n=31: 1145037275765491025924292050346,

1927890457142960697580636236639,

2309092682616190307509695338915

n=32: 17333509997782249308725103962772

@scythian: Do you have a prove that n=34 is an upper bound?

I think I can cover 34 digits with a few hours of calculation.

Edit: I upgraded my program and if i made no mistake n=50+ yields no results.

n=33:

186709961001538790100634132976990

186709961001538790100634132976991

n=34:

1122763285329372541592822900204593

So the maximum is either the one found for n=34 or one I didn't discover yet with n = 35..49

I think the limit is a 34-digit number. How to even find the maximum seems like a fun problem.

Edit: I now think the largest is much smaller than a 34-digit number, just from trying out a few numbers. The first few are as follows:

153

370

371

470

1634

8208

9474

54748

92727

93084

548834

1741725

4210818

9800817

9926315

24678050

24678051

More later.

Edit 2: No, MIchael, I don't think 34-digits is the upper bound any more. My initial hunch was off.

Is there any reason to limit these to numbers to base 10?

For example, 1^2 + 4^2 = 14 in base 13 which is 17 in base 10.

So you may or may not find a maximum for a particular base but I would imagine that there are an infinite number when expanded to any integer base b.

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