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Search: id:A020757
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| A020757 |
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Numbers that are not the sum of two triangular numbers. |
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+0
8
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| 5, 8, 14, 17, 19, 23, 26, 32, 33, 35, 40, 41, 44, 47, 50, 52, 53, 54, 59, 62, 63, 68, 71, 74, 75, 77, 80, 82, 85, 86, 89, 95, 96, 98, 103, 104, 107, 109, 113, 116, 117, 118, 122, 124, 125, 128, 129, 131, 134, 138, 140, 143, 145, 147, 149, 152, 155, 158, 161, 162, 166, 167
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A052343(a(n)) = 0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 15 2006
Numbers of the form (p^(2k+1)s-1)/4, where p is a prime number of the form 4n+3, and s is a number of the form 4m+3 and prime to p, are not expressible as the sum of two triangular numbers. See Satyanarayana (1961), Theorem 2. [From Hans Tuenter (htuenter(AT)gmail.com), Oct 11 2009]
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REFERENCES
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U. V. Satyanarayana. On the representation of numbers as sums of triangular numbers. The Mathematical Gazette, 45(351):40-43, February 1961. [From Hans Tuenter (htuenter(AT)gmail.com), Oct 11 2009]
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CROSSREFS
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Complement of A020756.
Sequence in context: A111321 A020736 A160421 this_sequence A049693 A084139 A092590
Adjacent sequences: A020754 A020755 A020756 this_sequence A020758 A020759 A020760
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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