A253260 Brazilian squares.

16, 36, 64, 81, 100, 121, 144, 196, 225, 256, 324, 400, 441, 484, 576, 625, 676, 729, 784, 900, 1024, 1089, 1156, 1225, 1296, 1444, 1521, 1600, 1764, 1936, 2025, 2116, 2304, 2401, 2500, 2601, 2704, 2916, 3025, 3136, 3249, 3364, 3600, 3844, 3969, 4096, 4225, 4356, 4624, 4761, 4900, 5184

Offset: 1

Author

Derek Orr, Apr 30 2015

Keywords

• nonn
• base

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

Intersection of A000290 and A125134. - Felix Fröhlich, 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

Examples

			From _Bernard Schott_, May 01 2017: (Start)
a(1) = 16 = 4^2 = 22_7.
a(6) = 121 = 11^2 = 11111_3. (End)
		

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.

Crossrefs

Cf. A000290, A125134.

Programs

Mathematica

fQ[n_]:=Module[{b=2, found=False}, While[b1, b++]; bVincenzo Librandi, May 02 2017 *)

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)))