This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A288783 #33 Jul 27 2020 04:46:01 %S A288783 7,8,10,12,13,14,16,20,22,27,33,34,35,38,39,43,46,51,55,58,65,69,73, %T A288783 74,77,81,82,87,94,95,106,115,118,119,121,122,123,125,127,134,141,142, %U A288783 143,145 %N A288783 Brazilian numbers which have only one Brazilian representation. %C A288783 These numbers could be called 1-Brazilian numbers. %C A288783 The smallest number of this sequence is 7 = 111_2 which is also the smallest Brazilian number (A125134) and the smallest Brazilian prime (A085104), and as such belongs to A329383. %C A288783 a(2) = 8 is the smallest composite Brazilian number and so the smallest even composite Brazilian with 8 = 22_3 (A220571). %C A288783 a(10) = 27 is the smallest odd composite Brazilian in this sequence because 27 = 33_8 but 15 is the smallest odd composite Brazilian with 15 = 1111_2 = 33_4 so with two representations. %C A288783 121 is the only square of prime which is Brazilian with 121 = 11111_3. %C A288783 In this sequence, there are: %C A288783 1) The Brazilian primes (except for 31 and 8191) and the only square of prime 121 which are all repunits in a base >= 2 with a string of at least three 1's. %C A288783 2) The composite numbers which are such that n = a * b = (aa)_(b-1) with 1 < a < b-1 with only one such product a * b. %D A288783 D. Lignon, Dictionnaire de (presque) tous les nombres entiers, Ellipses, 2012, page 420. %H A288783 Bernard Schott, <a href="/A125134/a125134.pdf">Les nombres brésiliens</a>, Quadrature, no. 76, avril-juin 2010, pages 30-38. %e A288783 13 = 111_3; 127 = 1111111_2. %e A288783 20 = 2 * 10 = 22_9; 55 = 5 * 11 = 55_10; 69 = 3 * 23 = 33_22. %e A288783 31 = 11111_2 = 111_5 so 31 is not a term. %t A288783 Select[Range@ 145, Function[n, Count[Range[2, n - 2], b_ /; SameQ @@ IntegerDigits[n, b]] == 1]] (* _Michael De Vlieger_, Jun 16 2017 *) %Y A288783 Cf. A085104, A125134, A220570, A220571, A284758, A290015, A290016, A290017, A290018, A329383. %K A288783 nonn,base,easy %O A288783 1,1 %A A288783 _Bernard Schott_, Jun 15 2017