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A120864
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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 = 12*n^2.
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2
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2, 3, 2, 12, 11, 8, 3, 23, 18, 11, 2, 32, 23, 12, 50, 39, 26, 11, 59, 44, 27, 8, 66, 47, 26, 3, 71, 48, 23, 99, 74, 47, 18, 104, 75, 44, 11, 107, 74, 39, 2, 108, 71, 32, 146, 107, 66, 23, 147, 104, 59, 12, 146, 99, 50, 192, 143, 92, 39, 191, 138, 83, 26, 188, 131, 72, 11, 183
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OFFSET
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1,1
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COMMENTS
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The k's that match these j's comprise A120865.
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LINKS
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FORMULA
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a(n) = 3*n^2 - floor(n*sqrt(3))^2.
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EXAMPLE
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a(1) = 3*1^2 - floor(1*sqrt(3))^2 = 2;
a(2) = 3*2^2 - floor(2*sqrt(3))^2 = 3;
a(3) = 3*3^2 - floor(3*sqrt(3))^2 = 2; etc.
Moreover,
for n = 1, the unique (j,k) is (2,1): (2+1+1)^2 - 4*1 = 12*1;
for n = 2, the unique (j,k) is (3,4): (3+4+1)^2 - 4*4 = 12*4;
for n = 3, the unique (j,k) is (2,9): (2+9+1)^2 - 4*9 = 12*9.
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PROG
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(PARI) a(n) = 3*n^2 - sqrtint(3*n^2)^2; \\ Michel Marcus, Jul 10 2020
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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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