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

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!)
 A290015 Brazilian numbers which have exactly two Brazilian representations. 3
 15, 18, 21, 26, 28, 30, 31, 32, 44, 45, 50, 52, 56, 57, 62, 64, 68, 75, 76, 85, 86, 91, 92, 93, 98, 99, 110, 111, 116, 117, 129, 133, 146, 147, 148, 153, 164, 175, 183, 188, 207, 212, 215, 219, 236, 243, 244, 245, 259, 261, 268, 275, 279, 284, 314, 316, 325, 332, 338, 341, 343, 356, 363, 365, 369, 381, 387, 388 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These numbers could be called 2-Brazilian numbers. The smallest number of this sequence is 15 which is also the smallest odd composite Brazilian in A257521 with 15 = 11111_2 = 33_4. The number 15 is of course highly Brazilian in A066044. Following the Goormaghtigh conjecture, only two primes, 31 and 8191, which are both Mersenne numbers, are Brazilian in two different bases (A119598). LINKS Wikipedia, Goormaghtigh conjecture EXAMPLE 18 = 2 * 9 = 22_8 = 3 * 6 = 33_5. 26 = 2 * 13 = 2 * 111_3 = 222_3 = 22_12. 31 = 11111_2 = 111_5; 8191 = 1111111111111_2 = 111_90. MAPLE bresilienbaseb:=proc(n, b) local r, q, coupleq: if n0 then return [couple[1]+1, r] else return [0, 0] end if end if end proc; bresil:=proc(n) local b, L, k, t: k:=0: for b from 2 to (n-2) do t:=bresilienbase(n, b): if t[1]>0 then k:=k+1 L[k]:=[b, t[1], t[2]]: end if: end do: seq(L[i], i=1..k); end proc; nbbresil:=n->nops([bresil(n)]); #Numbers 2 times Brazilian for n from 1 to 100 do if nbbresil(n)=2 then print(n, bresil(n)) else fi; od: MATHEMATICA Flatten@ Position[#, 2] &@ Table[Count[Range[2, n - 2], _?(And[Length@ # != 1, Length@ Union@ # == 1] &@ IntegerDigits[n, #] &)], {n, 400}] (* Michael De Vlieger, Jul 18 2017 *) CROSSREFS Cf. A066044, A085104, A125134, A220570, A220571, A257521, A284758, A288783, A290016, A290017, A290018. Sequence in context: A063781 A125006 A125008 * A274979 A083823 A222682 Adjacent sequences:  A290012 A290013 A290014 * A290016 A290017 A290018 KEYWORD nonn,base AUTHOR Bernard Schott, Jul 17 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.

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