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Search: id:A136359
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| A136359 |
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Perfect squares in A133459; or perfect squares that are the sums of two nonzero pentagonal pyramidal numbers. |
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3
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| 36, 81, 144, 289, 484, 576, 625, 676, 3600, 7396, 9801, 14400, 35344, 40000, 40804, 44100, 45796, 56644, 59049, 71824, 112896, 121104, 172225, 226576, 231361, 254016, 274576, 290521, 319225, 362404, 480249, 495616, 518400, 527076, 535824
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Corresponding numbers m such that m^2 = a(n) are listed in A136360 = {6,9,12,17,22,24,25,26,60,86,99,120,188,200,202,210,214,238,243,268,336,348, 415,476,481,504,524,539,565,602,693,704,720,726,732,846,899,961,...}. Note that some numbers in A136360 are also the perfect squares: m = k^2 = {9, 25, 961, 17424, ...}. The corresponding numbers k such that m = k^2 are listed in A136361 = {3, 5, 31, 132, ...}.
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FORMULA
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a(n) = A136360(n)^2.
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EXAMPLE
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A133459 begins {2,7,12,19,24,36,41,46,58,76,80,81,93,115,127,132,144,150,166,197,201,202,214,236,252,271,289,...}.
Thus a(1) = 36, a(2) = 81, a(3) = 144, a(4) = 289 that are the perfect squares in A133459.
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MATHEMATICA
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Select[ Intersection[ Flatten[ Table[ i^2*(i+1)/2 + j^2*(j+1)/2, {i, 1, 300}, {j, 1, i} ] ] ], IntegerQ[ Sqrt[ # ] ] & ]
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CROSSREFS
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Cf. A136360, A136361, A133459, A002311, A002411, A053721.
Adjacent sequences: A136356 A136357 A136358 this_sequence A136360 A136361 A136362
Sequence in context: A025399 A034813 A111163 this_sequence A084006 A043183 A039360
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Dec 25 2007
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