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%I #31 Jul 30 2017 12:53:04
%S 46,102,180,280,402,546,712,900,12433,99014,333669,790324,1542905,
%T 2665338,4231549,6315464,8991009,1372566064,21951169110,111111117780,
%U 351139655860,857235962280,1777511151114,3292988271580,5617602308040
%N Brazilian numbers whose repdigits are the same as the repdigits of the base.
%C These numbers could be called Super-Brazilian numbers. 11_11 = 12 is not a term because every number 11_(n-1) = n is not a Brazilian representation.
%C The super-Brazilian primes are of the form (R_p)_(R_p) where R_p is a Repunit of p 1's, with p prime. The first one is 111_111 = 12433, but 11111_11111 = 15242341197997105 is composite.
%H Gérard Villemin, <a href="http://villemin.gerard.free.fr/Wwwgvmm/Formes/RepDigit.htm#super">Nombres super-repdigits</a>, Dictionnaire des Nombres.
%e 22_22 = 2 * 22^1 + 2 * 22^0 = 44 + 2 = 46;
%e 444_444 = 4 * 444^2 + 4 * 444^1 + 4 * 444^0 = 788544 + 1776 + 4 = 790324.
%t Select[Range[10^3], Function[n, AnyTrue[Range[2, n - 2], Function[b, And[Length@ Union@ IntegerDigits[n, b] == 1, n == Total@ MapIndexed[#1 b^(First[#2] - 1) &, Reverse@ IntegerDigits[b]]]]]]] (* or, faster *)
%t Rest@ Flatten@ Table[Function[{m, d}, Total@ MapIndexed[#1 m^(First[#2] - 1) &, Reverse@ d]] @@ {FromDigits@ #, #} &@ ConstantArray[k, n], {n, 2, 4}, {k, 9}] (* _Michael De Vlieger_, Jun 01 2017 *)
%Y Cf. A002275, A085104, A125134.
%K nonn,base
%O 1,1
%A _Bernard Schott_, May 31 2017
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