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%I #32 Jul 27 2020 14:54:46
%S 60,80,84,96,108,126,140,150,156,160,198,200,204,220,224,234,255,260,
%T 273,276,294,308,315,340,342,348,350,352,372,392,414,416,460,476,486,
%U 490,492,495,500,516,522,525,544,550,558,564,572,580,608,620,636,644,675,693,708,726,735,736
%N Numbers with exactly five Brazilian representations: bases 1 < b_1 < b_2 < b_3 < b_4 < b_5 < n-1 such that n is a repdigit in base b_i.
%C These numbers could be called 5-Brazilian numbers.
%C All these numbers are composite with 8 to 13 divisors.
%C The smallest term is 60 and as such is a highly Brazilian number that belongs to A329383.
%H Charles R Greathouse IV, <a href="/A290018/b290018.txt">Table of n, a(n) for n = 1..10000</a>
%e 60 = 66_9 = 55_11 = 44_14 = 33_19 = 22_29 and tau(60) = 12.
%e 80 = 2222_3 = 22_39 = 44_19 = 55_15 = 88_9 and tau(80) = 10.
%e 255 = 11111111_2 = 3333_4 = 33_84 = 55_50 = (15 15)_16 and tau(255) = 8.
%e 4096 = (32 32)_127 = (16 16)_255 = 88_511 = 44_1023 = 22_2047 and tau(4096) = 13.
%t Flatten@ Position[#, 5] &@ Table[Count[Range[2, n - 2], _?(And[Length@ # != 1, Length@ Union@ # == 1] &@ IntegerDigits[n, #] &)], {n, 750}] (* _Michael De Vlieger_, Aug 09 2017 *)
%o (PARI) is(n)=my(d,ct); for(b=2, n-2, d=digits(n, b); for(i=2, #d, if(d[i]!=d[i-1], next(2))); if(ct++>5, return(0))); ct==5 \\ _Charles R Greathouse IV_, Aug 09 2017
%Y k-Brazilian numbers: A220570 (0), A288783 (1), A290015 (2), A290016 (3), A290017 (4), this sequence (5).
%Y Cf. A125134, A257521, A329383.
%K nonn,base
%O 1,1
%A _Bernard Schott_, Aug 07 2017
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