OFFSET
1,1
COMMENTS
Trivially, all even squares > 4 will be in this sequence.
The only square of a prime which is Brazilian is 121. - Bernard Schott, May 01 2017
Conjecture: Let r(n) = (a(n) - 1)/(a(n) + 1); then Product_{n>=1} r(n) = (15/17) * (35/37) * (63/65) * (40/41) * (99/101) * (60/61) * (143/145) * (195/197) * ... = (150 * Pi) / (61 * sinh(Pi)) = 0.668923905.... - Dimitris Valianatos, Feb 27 2019
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..405
Bernard Schott, Les nombres brésiliens Quadrature, no. 76, avril-juin 2010, théorème 5, page 37.
EXAMPLE
From Bernard Schott, May 01 2017: (Start)
a(1) = 16 = 4^2 = 22_7.
a(6) = 121 = 11^2 = 11111_3. (End)
MATHEMATICA
fQ[n_]:=Module[{b=2, found=False}, While[b<n-1&&Length[Union[IntegerDigits[n, b]]]>1, b++]; b<n-1]; Select[Range[1, 80]^2, fQ] (* Vincenzo Librandi, May 02 2017 *)
PROG
(PARI) for(n=4, 10^4, for(b=2, n-2, d=digits(n, b); if(vecmin(d)==vecmax(d)&&issquare(n), print1(n, ", "); break)))
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Derek Orr, Apr 30 2015
STATUS
approved