A290017 Brazilian numbers which have exactly four Brazilian representations.

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

Offset

1,1

Comments

These numbers could be called 4-Brazilian 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 A329383.

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, 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

Crossrefs

Cf. A125134, A220570, A220571, A257521, A288783, A290015, A290016, A290018, A329383.

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