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Search: id:A137693
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| A137693 |
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Numbers n such that 3n^2-n=6k^2-2k for some integer k>0. |
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+0
2
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| 7, 7887, 9101399, 10503006367, 12120460245927, 13987000620793199, 16140986595935105527, 18626684544708490984767, 21495177823607002661315399, 24805416581757936362666985487
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also indices of pentagonal numbers which are twice some other pentagonal number.
Note that A000326(n) = 2 A000326(k) <=> n(3n-1)=2k(3k-1), which is easily solved by standard Pell-type techniques (cf. link to D.Alpern's quadratic solver). Here we consider only positive solutions.
Inspired by a recent comment on A000326 by R. J. Mathar.
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LINKS
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D. Alpern, Quadratic two integer variable equation solver
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FORMULA
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a(n) = f^{2n-2}(5,7)[2], where f(x,y) = (577x + 408y - 164, 816x + 577y - 232)
a(n) = (7,7,9,7,7,9,...) mod 10
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PROGRAM
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(PARI) vector(20, i, (v=if(i>1, [577, 408; 816, 577]*v-[164; 232], [5; 7]))[2, 1])
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CROSSREFS
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Cf. A000326, A136112-A136118, A135768-A135769, A135771, A137694.
Sequence in context: A119528 A116266 A023344 this_sequence A116631 A074489 A067248
Adjacent sequences: A137690 A137691 A137692 this_sequence A137694 A137695 A137696
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KEYWORD
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easy,nonn
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AUTHOR
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M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Feb 08 2008
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