|
%I #19 Jul 31 2017 03:23:02
%S 8,10,12,14,15,16,18,20,21,22,24,26,27,28,30,32,33,34,35,36,38,39,40,
%T 42,44,45,46,48,50,51,52,54,55,56,57,58,60,62,63,64,65,66,68,69,70,72,
%U 74,75,76,77,78,80,81,82,84,85,86,87,88,90,91,92,93,94,95,96,98,99,100
%N Composite numbers that are Brazilian.
%C There are just two differences of members with A080257:
%C 1) the term 6 is missing here because 6 is not a Brazilian number.
%C 2) the new term 121 is present although 121 has only 3 divisors, because 121 = 11^2 = 11111_3 is a composite number which is Brazilian. 121 is the lone square of a prime which is Brazilian: Theorem 5, page 37 of Quadrature article in links.
%C There is an infinity of Brazilian composite numbers (Theorem 1, page 32 of Quadrature article in links: every even number >= 8 is a Brazilian number).
%H Michael De Vlieger, <a href="/A220571/b220571.txt">Table of n, a(n) for n = 1..10000</a>
%H Bernard Schott, <a href="/A125134/a125134.pdf">Les nombres brésiliens</a>, Quadrature, no. 76, avril-juin 2010, pages 30-38; included here with permission from the editors of Quadrature.
%t Select[Range[4, 10^2], And[CompositeQ@ #, Module[{b = 2, n = #}, While[And[b < n - 1, Length@ Union@ IntegerDigits[n, b] > 1], b++]; b < n - 1]] &] (* _Michael De Vlieger_, Jul 30 2017, after _T. D. Noe_ at A125134 *)
%Y Cf. A125134, A190300.
%K nonn
%O 1,1
%A _Bernard Schott_, Dec 16 2012
|
