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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. 45
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

9-th 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,changed

AUTHOR

Bernard Schott, Jan 21 2007

EXTENSIONS

More terms from Nathaniel Johnston, May 24 2011

STATUS

approved

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Last modified August 22 07:02 EDT 2017. Contains 290943 sequences.