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Search: id:A124934
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| A124934 |
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Numbers of the form 4mn - m - n, where m, n are positive integers. |
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+0
6
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| 2, 5, 8, 11, 12, 14, 17, 19, 20, 23, 26, 29, 30, 32, 33, 35, 38, 40, 41, 44, 47, 50, 52, 53, 54, 56, 59, 61, 62, 63, 65, 68, 71, 74, 75, 77, 80, 82, 83, 85, 86, 89, 90, 92, 95, 96, 98, 101, 103, 104, 107, 109, 110, 113, 116, 117, 118, 119, 122, 124, 125, 128, 129, 131
(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) misses the squares since (2x)^2 + 1 = (4m - 1)(4n - 1) is impossible.
a(n) misses the triangular numbers since (2x + 1)^2 + 1 = 2(4m - 1)(4n - 1) is impossible.
Taking m = k(k - 1)/2, n = k(k + 1)/2 gives 4mn - m - n = (k^2 - 1)^2 - 1, so a(n) is one less than a square infinitely often.
Complement of A094178; A125203(a(n)) > 0; union of A125217 and A125218; range of A125199. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 24 2006
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REFERENCES
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L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine Analysis. Dover Publications, Inc., Mineola, NY, 2005, p. 401.
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LINKS
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N. Hobson, Table of n, a(n) for n = 1..1000
N. Hobson, Home page (listed in lieu of email address)
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EXAMPLE
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a(1) = 2 because 2 = 4*1*1 - 1 - 1 is the smallest value in the sequence.
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CROSSREFS
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Cf. A000290, A000217.
Sequence in context: A143263 A102624 A070328 this_sequence A125217 A083422 A167409
Adjacent sequences: A124931 A124932 A124933 this_sequence A124935 A124936 A124937
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KEYWORD
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easy,nonn
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AUTHOR
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Nick Hobson Nov 13 2006
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EXTENSIONS
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More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 24 2006
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