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A253260 Brazilian squares. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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

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

Cf. A000290, A125134.

Sequence in context: A066112 A223456 A103843 * A144548 A161753 A062312

Adjacent sequences:  A253257 A253258 A253259 * A253261 A253262 A253263

KEYWORD

nonn,base

AUTHOR

Derek Orr, Apr 30 2015

STATUS

approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)