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A120866
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a(n) is the number j for which there exists a unique pair (j,k) of positive integers such that (j + k + 1)^2 - 4*k = 20*n^2.
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2
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1, 4, 9, 16, 4, 11, 20, 31, 5, 16, 29, 44, 4, 19, 36, 55, 1, 20, 41, 64, 89, 19, 44, 71, 100, 16, 45, 76, 109, 11, 44, 79, 116, 4, 41, 80, 121, 164, 36, 79, 124, 171, 29, 76, 125, 176, 20, 71, 124, 179, 9, 64, 121, 180, 241, 55, 116, 179, 244, 44, 109, 176, 245, 31, 100
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OFFSET
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1,2
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COMMENTS
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The k's that match these j's comprise A120867.
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LINKS
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FORMULA
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a(n) = 5*n^2 - floor(n*sqrt(5))^2.
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EXAMPLE
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1 = 5*1 - floor(sqrt(5))^2,
4 = 5*4 - floor(2*sqrt(5))^2,
9 = 5*9 - floor(3*sqrt(5))^2, etc.
Moreover,
for n = 1, the unique (j,k) is (1,4): (1 + 4 + 1)^2 - 4*4 = 20*1;
for n = 2, the unique (j,k) is (4,5): (4 + 5 + 1)^2 - 4*5 = 20*4;
for n = 3, the unique (j,k) is (9,4): (9 + 4 + 1)^2 - 4*4 = 20*9.
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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