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Search: id:A129445
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| A129445 |
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Numbers k>0 such that k^2 is a centered triangular number. |
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3
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| 1, 2, 8, 19, 79, 188, 782, 1861, 7741, 18422, 76628, 182359, 758539, 1805168, 7508762, 17869321, 74329081, 176888042, 735782048, 1751011099, 7283491399, 17333222948, 72099131942, 171581218381, 713707828021, 1698478960862
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OFFSET
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1,2
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COMMENT
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Corresponding numbers n such that centered triangular number A005448(n) = 3n(n-1)/2 + 1 is a perfect square are listed in A129444(n) = {1,2,7,16,65,154,639,1520,6321,15042,62567,148896,...}.
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LINKS
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Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 26 2007, Table of n, a(n) for n = 1..100
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FORMULA
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a(n) = Sqrt[ 3*A129444(n)*(A129444(n) - 1)/2 + 1 ].
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MATHEMATICA
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Do[ f = 3n(n-1)/2 + 1; If[ IntegerQ[ Sqrt[f] ], Print[ Sqrt[f] ] ], {n, 1, 150000} ]
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CROSSREFS
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Cf. A005448 = Centered triangular numbers: 3n(n-1)/2 + 1. Cf. A129444 = numbers n such that centered triangular number A005448(n) = 3n(n-1)/2 + 1 is a perfect square.
Prime terms are listed in A129446(n) = {2,19,79,1861,7741,...}.
Sequence in context: A026588 A026572 A074797 this_sequence A082821 A030097 A136904
Adjacent sequences: A129442 A129443 A129444 this_sequence A129446 A129447 A129448
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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), Apr 15 2007, Apr 26 2007
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EXTENSIONS
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More terms from Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 26 2007
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