A220571 Composite numbers that are Brazilian.

8, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100

Offset

1,1

Comments

There are just two differences of members with A080257:

1) the term 6 is missing here because 6 is not a Brazilian number.

2) the new term 121 is present although 121 has only 3 divisors, because 121 = 11^2 = 11111_3 is a composite number which is Brazilian. 121 is the lone square of a prime which is Brazilian: Theorem 5, page 37 of Quadrature article in links.

There is an infinity of Brazilian composite numbers (Theorem 1, page 32 of Quadrature article in links: every even number >= 8 is a Brazilian number).

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38; included here with permission from the editors of Quadrature.

Mathematica

Select[Range[4, 10^2], And[CompositeQ@ #, Module[{b = 2, n = #}, While[And[b < n - 1, Length@ Union@ IntegerDigits[n, b] > 1], b++]; b < n - 1]] &] (* Michael De Vlieger, Jul 30 2017, after T. D. Noe at A125134 *)

Crossrefs

Cf. A125134, A190300.

Sequence in context: A338473 A336143 A347267 * A033872 A080752 A262159

Adjacent sequences: A220568 A220569 A220570 * A220572 A220573 A220574

Keyword

nonn

Author

Bernard Schott, Dec 16 2012

Status

approved