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

Author

Bernard Schott, Jul 28 2017

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

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