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Search: id:A145856
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| A145856 |
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Least number k>1 such that centered n-gonal number n*k(k-1)/2+1 is a perfect square. |
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+0
1
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| 3, 0, 2, 4, 3, 8, 16, 2, 17, 9, 15, 5, 6, 16, 2, 3, 6, 0, 7, 4, 3, 40, 7, 2, 22, 8, 111, 4, 16, 8, 16, 0, 3, 9, 2, 5, 990, 9, 15, 3, 46, 16, 10, 5, 6, 336, 10, 2, 30, 0, 31, 16, 11, 416, 7, 3, 11, 33, 55, 4, 78, 56, 2, 6, 3, 8, 47751, 12, 16, 24, 48, 0, 49, 25, 17, 13, 6, 9, 2640, 2, 6721
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n) = 0 for n = {2, 18, 32, 50, 72, 98, ...} which appear to be all numbers of the form of 2*m^2, except for m=2. Note an unusually large outlier a(67) = 47751.
a(n) = A120744(n) + 1. [From Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 10 2009]
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REFERENCES
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Jonathan Vos Post, When Centered Polygonal Numbers are Perfect Squares, submitted to Mathematics Magazine, 4 May 2004, manuscript no. 04-1165, unpublished, available upon request [From Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 25 2008]
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LINKS
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E. Weisstein, MathWorld, Centered Polygonal Numbers
Index entries for sequences related to centered polygonal numbers
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CROSSREFS
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Cf. A120744, A001542, A166259, A006451, A001921, A129444, A001570, A001652, A129556, A053606, A105038, A105040, A053141, A061278. [From Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 10 2009]
Sequence in context: A113069 A136163 A058624 this_sequence A092154 A139585 A089598
Adjacent sequences: A145853 A145854 A145855 this_sequence A145857 A145858 A145859
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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), Oct 22 2008
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