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A253260
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Brazilian squares.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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a(1) = 16 = 4^2 = 22_7.
a(6) = 121 = 11^2 = 11111_3. (End)
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MATHEMATICA
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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 *)
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PROG
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(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)))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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