

A290017


Brazilian numbers which have exactly four Brazilian representations.


4



40, 48, 63, 72, 90, 112, 114, 132, 162, 170, 176, 208, 222, 266, 285, 304, 306, 366, 368, 380, 399, 405, 438, 455, 464, 496, 512, 518, 555, 567, 592, 650, 651, 656, 665, 682, 686, 688, 752, 762, 812, 848, 891, 915, 931, 942, 944, 976, 992, 999, 1024, 1029, 1053, 1072, 1106, 1136, 1168
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OFFSET

1,1


COMMENTS

These numbers could be called 4Brazilian numbers.
All these numbers are composite with six to twelve divisors.
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.


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


EXAMPLE

48 = 6 * 8 = 66_7 = 4 * 12 = 44_11 = 3 * 16 = 33_15 = 2 * 24 = 22_23.
63 = 111111_2 = 3 * 21 = 33_20 = 333_4 = 7 * 9 = 77_8.


MATHEMATICA

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 *)


PROG

(PARI) is(n)=my(d, ct); for(b=2, n2, d=digits(n, b); for(i=2, #d, if(d[i]!=d[i1], next(2))); if(ct++>4, return(0))); ct==4 \\ Charles R Greathouse IV, Aug 10 2017


CROSSREFS

Cf. A066044, A125134, A220570, A220571, A257521, A288783, A290015, A290016, A290018.
Sequence in context: A114839 A179435 A120382 * A062909 A167327 A216305
Adjacent sequences: A290014 A290015 A290016 * A290018 A290019 A290020


KEYWORD

nonn,base


AUTHOR

Bernard Schott, Jul 28 2017


STATUS

approved



