A257521 Odd Brazilian numbers.

7, 13, 15, 21, 27, 31, 33, 35, 39, 43, 45, 51, 55, 57, 63, 65, 69, 73, 75, 77, 81, 85, 87, 91, 93, 95, 99, 105, 111, 115, 117, 119, 121, 123, 125, 127, 129, 133, 135, 141, 143, 145, 147, 153, 155, 157, 159, 161, 165, 171, 175, 177, 183, 185, 187, 189, 195

Offset: 1

Author

Daniel Lignon, Apr 27 2015

Keywords

• nonn
• base
• easy

Comments

All even integers 2p >=8 are Brazilian numbers (A125134), because 2p=2(p-1)+2 is written 22 in base p-1 if p-1>2, that is true if p >=4. But, among Brazilian numbers, there are also odd ones...

The only square of a prime is 121. - Robert G. Wilson v, May 21 2015

Links

• Daniel Lignon and Robert Israel, Table of n, a(n) for n = 1..10000 (first 703 from Daniel Lignon)

Crossrefs

Cf. A125134 (Brazilian numbers), A253261 (odd Brazilian squares).

Cf. A085104 (prime Brazilian numbers).

Programs

Maple

N:= 1000: # to get all terms <= N
for b from 2 to floor(N/2-1) do
   dk:= 1 + (b mod 2);
   for j from 1 to b-1 by 2 do
     for k from dk by dk do
       if j=1 and k=1 then next fi;
       x:= j*(b^(k+1)-1)/(b-1);
       if x > N then break fi;
       B[x]:= 1;
     od
   od
od:
sort(map(op,[indices(B)])); # Robert Israel, May 27 2015

Mathematica

fQ[n_] := Block[{b = 2}, While[b < n - 1 && Length[ Union[ IntegerDigits[n, b]]] > 1, b++]; b < n - 1]; Select[1 + 2 Range@100, fQ] (* Robert G. Wilson v, May 21 2015 *)

PARI

forstep(n=5, 300, 2, for(b=2, n-2, d=digits(n, b); if(vecmin(d)==vecmax(d), print1(n, ", "); break))) \\ Derek Orr, Apr 30 2015