A290018 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.

60, 80, 84, 96, 108, 126, 140, 150, 156, 160, 198, 200, 204, 220, 224, 234, 255, 260, 273, 276, 294, 308, 315, 340, 342, 348, 350, 352, 372, 392, 414, 416, 460, 476, 486, 490, 492, 495, 500, 516, 522, 525, 544, 550, 558, 564, 572, 580, 608, 620, 636, 644, 675, 693, 708, 726, 735, 736

Offset: 1

Author

Bernard Schott, Aug 07 2017

Keywords

• nonn
• base

Comments

These numbers could be called 5-Brazilian numbers.

All these numbers are composite with 8 to 13 divisors.

The smallest term is 60 and as such is a highly Brazilian number that belongs to A329383.

Examples

			60 = 66_9 = 55_11 = 44_14 = 33_19 = 22_29 and tau(60) = 12.
80 = 2222_3 = 22_39 = 44_19 = 55_15 = 88_9 and tau(80) = 10.
255 = 11111111_2 = 3333_4 = 33_84 = 55_50 = (15 15)_16 and tau(255) = 8.
4096 = (32 32)_127 = (16 16)_255 = 88_511 = 44_1023 = 22_2047 and tau(4096) = 13.
		

Links

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

Crossrefs

k-Brazilian numbers: A220570 (0), A288783 (1), A290015 (2), A290016 (3), A290017 (4), this sequence (5).

Cf. A125134, A257521, A329383.

Programs

Mathematica

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 *)

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