A288068 - OEIS

%I #23 Oct 02 2024 11:06:03

%S 7,8,22,33,44,55,66,77,88,99,111,222,333,444,555,666,777,888,999,1111,

%T 2222,3333,4444,5555,6666,7777,8888,9999,11111,22222,33333,44444,

%U 55555,66666,77777,88888,99999,111111,222222,333333,444444,555555,666666,777777,888888,999999

%N Repdigits in base 10 which are Brazilian numbers.

%C 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.

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

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, -10).

%e 7 = 111_2;

%e 44 = 44_10 = 22_21;

%e 66 = 66_10 = 33_21 = 22_32.

%p # reuses code of A125134, b-file output

%p n := 1 :

%p for ndigs from 1 do

%p     for d from 1 to 9 do

%p         r := add(d*10^i,i=0..ndigs-1) ; # rep digit d in base 10

%p         if isA125134(r) then

%p             printf("%d %d\n",n,r) ;

%p             n := n+1 ;

%p         end if;

%p     end do:

%p end do: # _R. J. Mathar_, Jul 19 2024

%t 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 *)

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

%K nonn,base

%O 1,1

%A _Bernard Schott_, Jun 05 2017