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A287767 Brazilian numbers whose repdigits are the same as the repdigits of the base. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A252695 A252688 A119417 * A050961 A264445 A248529

Adjacent sequences:  A287764 A287765 A287766 * A287768 A287769 A287770

KEYWORD

nonn,base

AUTHOR

Bernard Schott, May 31 2017

STATUS

approved

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Last modified August 11 05:13 EDT 2022. Contains 356046 sequences. (Running on oeis4.)