

A125134


"Brazilian" numbers ("les nombres brésiliens" in French): numbers n such that there is a natural number b with 1 < b < n1 such that the representation of n in base b has all equal digits.


41



7, 8, 10, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 42, 43, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90
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OFFSET

1,1


COMMENTS

The condition b < n1 is important because every number n has representation 11 in base n1.  Daniel Lignon, May 22 2015
Every even number >=8 is Brazilian. Odd Brazilian numbers are in A257521.  Daniel Lignon, May 22 2015
Looking at A190300, it seems that asymptotically 100% of composite numbers are Brazilian, while looking at A085104, it seems that asymptotically 0% of prime numbers are Brazilian. The asymptotic density of Brazilian numbers would thus be 100%.  Daniel Forgues, Oct 07 2016


REFERENCES

Pierre Bornsztein, "Hypermath", Vuibert, Exercise a35, p. 7.
Iberoamerican Olympiads, 1994.


LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..4000
Bernard Schott and others, Postings to the French mathematical forum lesmathematiques.net
Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avriljuin 2010, pages 3038; included here with permission from the editors of Quadrature.


EXAMPLE

15 is a member since it is 33 in base 4.


MAPLE

isA125134 := proc(n) local k: for k from 2 to n2 do if(nops(convert(convert(n, base, k), set))=1)then return true: fi: od: return false: end: A125134 := proc(n) option remember: local k: if(n=1)then return 7: fi: for k from procname(n1)+1 do if(isA125134(k))then return k: fi: od: end: seq(A125134(n), n=1..65); # Nathaniel Johnston, May 24 2011


MATHEMATICA

fQ[n_] := Module[{b = 2, found = False}, While[b < n  1 && Length[Union[IntegerDigits[n, b]]] > 1, b++]; b < n  1]; Select[Range[4, 90], fQ] (* T. D. Noe, May 07 2013 *)


PROG

(PARI) for(n=4, 100, for(b=2, n2, d=digits(n, b); if(vecmin(d)==vecmax(d), print1(n, ", "); break))) \\ Derek Orr, Apr 30 2015


CROSSREFS

Cf. A190300 and A257521 (odd Brazilian numbers).
Cf. A085104 (prime Brazilian numbers).
Sequence in context: A266727 A214004 A037263 * A169876 A288783 A120175
Adjacent sequences: A125131 A125132 A125133 * A125135 A125136 A125137


KEYWORD

nonn,base,easy


AUTHOR

Bernard Schott, Jan 21 2007


EXTENSIONS

More terms from Nathaniel Johnston, May 24 2011


STATUS

approved



