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 A290017 Brazilian numbers which have exactly four Brazilian representations. 4

%I

%S 40,48,63,72,90,112,114,132,162,170,176,208,222,266,285,304,306,366,

%T 368,380,399,405,438,455,464,496,512,518,555,567,592,650,651,656,665,

%U 682,686,688,752,762,812,848,891,915,931,942,944,976,992,999,1024,1029,1053,1072,1106,1136,1168

%N Brazilian numbers which have exactly four Brazilian representations.

%C These numbers could be called 4-Brazilian numbers.

%C All these numbers are composite with six to twelve divisors.

%C The smallest number of this sequence is 40 with 40 = 1111_3 = 55_7 = 44_9 = 22_19. The number 40 is a highly Brazilian number in A066044.

%H Charles R Greathouse IV, <a href="/A290017/b290017.txt">Table of n, a(n) for n = 1..10000</a>

%e 48 = 6 * 8 = 66_7 = 4 * 12 = 44_11 = 3 * 16 = 33_15 = 2 * 24 = 22_23.

%e 63 = 111111_2 = 3 * 21 = 33_20 = 333_4 = 7 * 9 = 77_8.

%t Flatten@ Position[#, 4] &@ Table[Count[Range[2, n - 2], _?(And[Length@ # != 1, Length@ Union@ # == 1] &@ IntegerDigits[n, #] &)], {n, 10^3}] (* _Michael De Vlieger_, Jul 30 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++>4, return(0))); ct==4 \\ _Charles R Greathouse IV_, Aug 10 2017

%Y Cf. A066044, A125134, A220570, A220571, A257521, A288783, A290015, A290016, A290018.

%K nonn,base

%O 1,1

%A _Bernard Schott_, Jul 28 2017

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Last modified April 1 13:39 EDT 2020. Contains 333159 sequences. (Running on oeis4.)