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Search: id:A067274
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| A067274 |
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Number of ordered integer pairs (b,c), with -n<=b<=n, -n<=c<=n, such that both roots of x^2+bx+c=0 are integers. |
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+0
3
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| 1, 4, 10, 16, 25, 31, 41, 47, 57, 66, 76, 82, 96, 102, 112, 122, 135, 141, 155, 161, 175, 185, 195, 201, 219, 228, 238, 248, 262, 268, 286, 292, 306, 316, 326, 336, 357, 363, 373, 383, 401, 407, 425, 431, 445, 459, 469, 475, 497, 506, 520, 530, 544, 550, 568
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Conjecture: The difference a(n)-a(n-1) is 6 if and only if n is a prime number. This has been checked up to about n=300, and may be easy to prove.
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LINKS
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Eric Weisstein's World of Mathematics, Quadratic Equation
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FORMULA
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a(n) = a(n-1)+2*(tau(n)+1)+b(n), where b(n) = 1 if n is a square else 0 = 010052(n), n>1, a(1) = 4. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 05 2002
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CROSSREFS
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Sequence in context: A016957 A109273 A049881 this_sequence A054901 A019574 A095273
Adjacent sequences: A067271 A067272 A067273 this_sequence A067275 A067276 A067277
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Feb 21 2002
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