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A257521
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Odd Brazilian numbers.
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8
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Daniel Lignon and Robert Israel, Table of n, a(n) for n = 1..10000 (first 703 from Daniel Lignon)
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A125134 (Brazilian numbers), A253261 (odd Brazilian squares).
Cf. A085104 (prime Brazilian numbers).
Sequence in context: A349752 A167782 A326380 * A053696 A090503 A059520
Adjacent sequences: A257518 A257519 A257520 * A257522 A257523 A257524
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KEYWORD
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nonn,base,easy
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AUTHOR
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Daniel Lignon, Apr 27 2015
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STATUS
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approved
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