A287767 Brazilian numbers whose repdigits are the same as the repdigits of the base.

46, 102, 180, 280, 402, 546, 712, 900, 12433, 99014, 333669, 790324, 1542905, 2665338, 4231549, 6315464, 8991009, 1372566064, 21951169110, 111111117780, 351139655860, 857235962280, 1777511151114, 3292988271580, 5617602308040

Offset

1,1

Comments

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.

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.

Links

Table of n, a(n) for n=1..25.

Gérard Villemin, Nombres super-repdigits, Dictionnaire des Nombres.

Example

22_22 = 2 * 22^1 + 2 * 22^0 = 44 + 2 = 46;
444_444 = 4 * 444^2 + 4 * 444^1 + 4 * 444^0 = 788544 + 1776 + 4 = 790324.

Mathematica

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 *)
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 *)

Crossrefs

Cf. A002275, A085104, A125134.

Sequence in context: A252688 A358897 A119417 * A050961 A264445 A248529

Adjacent sequences: A287764 A287765 A287766 * A287768 A287769 A287770

Keyword

nonn,base

Author

Bernard Schott, May 31 2017

Status

approved