A288068 Repdigits in base 10 which are Brazilian numbers.

7, 8, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999, 111111, 222222, 333333, 444444, 555555, 666666, 777777, 888888, 999999

Offset

1,1

Comments

These numbers are all repdigits belonging to A010785. The representation of the numbers 7 and 8 in base 10 is not Brazilian but they are yet Brazilian because 7 = 111_2 and 8 = 22_3. Except the repdigits 7, 8, 22, 33, 55, 77 and the primes repunits R_n from A004022 and A004023, all these Brazilian repdigits are also Brazilian in another base.

Contains all base-10 repdigits (A010785) >= 22, because these are Brazilian numbers in base 10. - R. J. Mathar, Jul 19 2024

Links

Table of n, a(n) for n=1..46.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, -10).

Example

7 = 111_2;
44 = 44_10 = 22_21;
66 = 66_10 = 33_21 = 22_32.

Maple

# reuses code of A125134, b-file output
n := 1 :
for ndigs from 1 do
    for d from 1 to 9 do
        r := add(d*10^i, i=0..ndigs-1) ; # rep digit d in base 10
        if isA125134(r) then
            printf("%d %d\n", n, r) ;
            n := n+1 ;
        end if;
    end do:
end do: # R. J. Mathar, Jul 19 2024

Mathematica

Select[Flatten@ Table[FromDigits@ ConstantArray[k, n], {n, 6}, {k, 9}], Function[n, Length@ SelectFirst[Range[2, n - 2], Count[DigitCount[n, #], _?(# > 0 &)] == 1 &] == 0]] (* Michael De Vlieger, Jun 06 2017, Version 10 *)

Crossrefs

Cf. A004022, A004023, A010785, A014181, A125134,

Sequence in context: A051175 A322651 A325322 * A058537 A002362 A042417

Adjacent sequences: A288065 A288066 A288067 * A288069 A288070 A288071

Keyword

nonn,base

Author

Bernard Schott, Jun 05 2017

Status

approved