login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A288783 Brazilian numbers which have only one Brazilian representation. 4
7, 8, 10, 12, 13, 14, 16, 20, 22, 27, 33, 34, 35, 38, 39, 43, 46, 51, 55, 58, 65, 69, 73, 74, 77, 81, 82, 87, 94, 95, 106, 115, 118, 119, 121, 122, 123, 125, 127, 134, 141, 142, 143, 145 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

These numbers could be called 1-Brazilian numbers.

The smallest number of this sequence is 7 = 111_2 which is also the smallest Brazilian number (A125134) and so the smallest Brazilian prime (A085104).

a(2) = 8 is the smallest composite Brazilian number and so the smallest even composite Brazilian with 8 = 22_3 (A220571).

a(10) = 27 is the smallest odd composite Brazilian in this sequence because 27 = 33_8 but 15 is the smallest odd composite Brazilian with 15 = 1111_2 = 33_4 so with two representations.

121 is the only square of prime which is Brazilian with 121 = 11111_3.

In this sequence, there are:

1) The Brazilian primes and the lone square prime 121 which are all repunits in a base >= 2 with a string of at least three 1's.

2) The composite numbers which are such that n = a * b = (aa)_(b-1) with 1 < a < b-1 with only one such product a * b.

REFERENCES

D. Lignon, Dictionnaire de (presque) tous les nombres entiers, Ellipses, 2012, page 420.

LINKS

Table of n, a(n) for n=1..44.

Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38.

EXAMPLE

13 = 111_3; 127 = 1111111_2.

20 = 2 * 10 = 22_9; 55 = 5 * 11 = 55_10; 69 = 3 * 23 = 33_22.

MATHEMATICA

Select[Range@ 145, Function[n, Count[Range[2, n - 2], b_ /; SameQ @@ IntegerDigits[n, b]] == 1]] (* Michael De Vlieger, Jun 16 2017 *)

CROSSREFS

Cf. A085104, A125134, A190300, A220570, A220571, A253260, A284758.

Sequence in context: A037263 A125134 A169876 * A120175 A291668 A175222

Adjacent sequences:  A288780 A288781 A288782 * A288784 A288785 A288786

KEYWORD

nonn,base,easy

AUTHOR

Bernard Schott, Jun 15 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 22 10:25 EST 2020. Contains 331144 sequences. (Running on oeis4.)