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A257521 Odd Brazilian numbers. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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)

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 *)

PROG

(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

CROSSREFS

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

Cf. A085104 (prime Brazilian numbers).

Sequence in context: A076196 A167782 A326380 * A053696 A090503 A059520

Adjacent sequences:  A257518 A257519 A257520 * A257522 A257523 A257524

KEYWORD

nonn,base,easy

AUTHOR

Daniel Lignon, Apr 27 2015

STATUS

approved

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Last modified December 12 20:12 EST 2019. Contains 329961 sequences. (Running on oeis4.)