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 A290015 Brazilian numbers which have exactly two Brazilian representations. 4
 15, 18, 21, 26, 28, 30, 31, 32, 44, 45, 50, 52, 56, 57, 62, 64, 68, 75, 76, 85, 86, 91, 92, 93, 98, 99, 110, 111, 116, 117, 129, 133, 146, 147, 148, 153, 164, 175, 183, 188, 207, 212, 215, 219, 236, 243, 244, 245, 259, 261, 268, 275, 279, 284, 314, 316, 325, 332, 338, 341, 343, 356, 363, 365, 369, 381, 387, 388 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These numbers could be called 2-Brazilian numbers. The smallest number of this sequence is 15 which is also the smallest odd composite Brazilian in A257521 with 15 = 11111_2 = 33_4. The number 15 is highly Brazilian in A329383. Following the Goormaghtigh conjecture, only two primes, 31 and 8191, which are both Mersenne numbers, are Brazilian in two different bases (A119598). LINKS Table of n, a(n) for n=1..68. Wikipedia, Goormaghtigh conjecture EXAMPLE 18 = 2 * 9 = 22_8 = 3 * 6 = 33_5. 26 = 2 * 13 = 2 * 111_3 = 222_3 = 22_12. 31 = 11111_2 = 111_5; 8191 = 1111111111111_2 = 111_90. MAPLE bresilienbaseb:=proc(n, b) local r, q, coupleq: if n0 then return [couple[1]+1, r] else return [0, 0] end if end if end proc; bresil:=proc(n) local b, L, k, t: k:=0: for b from 2 to (n-2) do t:=bresilienbase(n, b): if t[1]>0 then k:=k+1 L[k]:=[b, t[1], t[2]]: end if: end do: seq(L[i], i=1..k); end proc; nbbresil:=n->nops([bresil(n)]); #Numbers 2 times Brazilian for n from 1 to 100 do if nbbresil(n)=2 then print(n, bresil(n)) else fi; od: MATHEMATICA Flatten@ Position[#, 2] &@ Table[Count[Range[2, n - 2], _?(And[Length@ # != 1, Length@ Union@ # == 1] &@ IntegerDigits[n, #] &)], {n, 400}] (* Michael De Vlieger, Jul 18 2017 *) CROSSREFS Cf. A085104, A125134, A220570, A220571, A257521, A284758, A288783, A290016, A290017, A290018, A329383. Sequence in context: A063779 A125006 A125008 * A354818 A274979 A083823 Adjacent sequences: A290012 A290013 A290014 * A290016 A290017 A290018 KEYWORD nonn,base AUTHOR Bernard Schott, Jul 17 2017 STATUS approved

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Last modified June 9 00:10 EDT 2023. Contains 363165 sequences. (Running on oeis4.)