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Search: id:A020756
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| A020756 |
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Numbers which are the sum of two triangular numbers. |
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+0
9
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| 0, 1, 2, 3, 4, 6, 7, 9, 10, 11, 12, 13, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 29, 30, 31, 34, 36, 37, 38, 39, 42, 43, 45, 46, 48, 49, 51, 55, 56, 57, 58, 60, 61, 64, 65, 66, 67, 69, 70, 72, 73, 76, 78, 79, 81, 83, 84, 87, 88, 90, 91, 92, 93, 94, 97, 99, 100, 101, 102, 105, 106, 108
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The possible sums of a square and a pronic, i.e. x^2+n(n+1), e.g. 3^2+2.3=9+6=15 is present. - Jon Perry (perry(AT)globalnet.co.uk), May 28 2003
A052343(a(n)) > 0; union of A118139 and A119345. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), May 15 2006
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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Numbers n such that 4n+1 is the sum of two squares, i.e. such that 4n+1 is in A001481. Hence n is a member if and only if 4n+1 = odd square * product of distinct primes of form 4k+1. (Fred Helenius and others, Dec 18 2004)
Closed under the operation f(x, y) = 4xy + x + y.
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PROGRAM
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(PARI) v=vector(200); vc=0; for (x=0, 10, for (y=0, 10, v[vc++ ]=x^2+y*(y+1))); v=vecsort(v); v
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CROSSREFS
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Complement of A020757.
Cf. A051533 (sums of two positive triangular numbers, A001481 (sums of two squares), A002378.
Sequence in context: A039148 A065904 A039108 this_sequence A051382 A026514 A039054
Adjacent sequences: A020753 A020754 A020755 this_sequence A020757 A020758 A020759
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KEYWORD
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nonn,nice
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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Entry revised by njas, Dec 20 2004
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