A220570 Numbers that are not Brazilian numbers.

1, 2, 3, 4, 5, 6, 9, 11, 17, 19, 23, 25, 29, 37, 41, 47, 49, 53, 59, 61, 67, 71, 79, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 277, 281

Offset: 1

Author

Bernard Schott, Dec 16 2012

Keywords

• nonn
• easy
• base

Comments

From Bernard Schott, Apr 23 2019: (Start)

The terms of this sequence are:

- integer 1

- oblong semiprime 6,

- primes that are not Brazilian, they are in A220627, and,

- squares of all the primes, except 121 = (11111)_3.

So there is an infinity of integers that are not Brazilian numbers. (End)

This sequence has density 0 as A125134(n) ~ n where A125134 is the complement of this sequence. - David A. Corneth, Jan 22 2021

Examples

			25 is a member because it's not possible to write 25=(mm...mm)_b where b is a natural number with 1 < b < 24 and 1 <= m < b.
		

References

• Pierre Bornsztein, "Hypermath", Vuibert, Exercise a35, page 7.

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
• Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, &6 page 36; included here with permission from the editors of Quadrature.

Crossrefs

Cf. A125134 (Brazilian numbers), A190300 (composite numbers not Brazilian), A258165 (odd numbers not Brazilian), A220627 (prime numbers not Brazilian).

Programs

PARI

for(n=1,300,c=0;for(b=2,n-2,d=digits(n,b);if(vecmin(d)==vecmax(d),c=n;break);c++);if(c==max(n-3,0),print1(n,", "))) \\ Derek Orr, Apr 30 2015