OFFSET
1,1
COMMENTS
The condition b < n-1 is important because every number n has representation 11 in base n-1. - 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.
LINKS
Nathaniel Johnston, Table of n, a(n) for n = 1..4000
9th Iberoamerican Mathematical Olympiad, Problem 1: sensible numbers, Fortaleza, Brazil, September 17-25, 1994.
Bernard Schott and others, Postings to the French mathematical forum les-mathematiques.net
Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38; included here with permission from the editors of Quadrature.
FORMULA
a(n) ~ n. - Charles R Greathouse IV, Aug 09 2017
EXAMPLE
15 is a member since it is 33 in base 4.
MAPLE
isA125134 := proc(n) local k: for k from 2 to n-2 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(n-1)+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, n-2, d=digits(n, b); if(vecmin(d)==vecmax(d), print1(n, ", "); break))) \\ Derek Orr, Apr 30 2015
(PARI) is(n)=my(m); if(!isprime(n), return(if(issquare(n, &m), m>3 && (!isprime(m) || m==11), n>6))); for(b=2, n-2, m=digits(n, b); for(i=2, #m, if(m[i]!=m[i-1], next(2))); return(1)); 0 \\ Charles R Greathouse IV, Aug 09 2017
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Bernard Schott, Jan 21 2007
EXTENSIONS
More terms from Nathaniel Johnston, May 24 2011
STATUS
approved