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A257521 Odd Brazilian numbers.

%I A257521 #32 Oct 08 2016 02:31:37
%S A257521 7,13,15,21,27,31,33,35,39,43,45,51,55,57,63,65,69,73,75,77,81,85,87,
%T A257521 91,93,95,99,105,111,115,117,119,121,123,125,127,129,133,135,141,143,
%U A257521 145,147,153,155,157,159,161,165,171,175,177,183,185,187,189,195
%N A257521 Odd Brazilian numbers.
%C A257521 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...
%C A257521 The only square of a prime is 121. - _Robert G. Wilson v_, May 21 2015
%H A257521 Daniel Lignon and Robert Israel, <a href="/A257521/b257521.txt">Table of n, a(n) for n = 1..10000</a> (first 703 from Daniel Lignon)
%p A257521 N:= 1000: # to get all terms <= N
%p A257521 for b from 2 to floor(N/2-1) do
%p A257521    dk:= 1 + (b mod 2);
%p A257521    for j from 1 to b-1 by 2 do
%p A257521      for k from dk by dk do
%p A257521        if j=1 and k=1 then next fi;
%p A257521        x:= j*(b^(k+1)-1)/(b-1);
%p A257521        if x > N then break fi;
%p A257521        B[x]:= 1;
%p A257521      od
%p A257521    od
%p A257521 od:
%p A257521 sort(map(op,[indices(B)])); # _Robert Israel_, May 27 2015
%t A257521 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 *)
%o A257521 (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
%Y A257521 Cf. A125134 (Brazilian numbers), A253261 (odd Brazilian squares).
%Y A257521 Cf. A085104 (prime Brazilian numbers).
%K A257521 nonn,base,easy
%O A257521 1,1
%A A257521 _Daniel Lignon_, Apr 27 2015