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 A125134 "Brazilian" numbers ("les nombres brésiliens" in French): numbers n such that there is a natural number b with 1 < b < n-1 such that the representation of n in base b has all equal digits. 56
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified July 4 02:21 EDT 2020. Contains 335436 sequences. (Running on oeis4.)