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A114948
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a(n) = n^2 + 10.
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4
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11, 14, 19, 26, 35, 46, 59, 74, 91, 110, 131, 154, 179, 206, 235, 266, 299, 334, 371, 410, 451, 494, 539, 586, 635, 686, 739, 794, 851, 910, 971, 1034, 1099, 1166, 1235, 1306, 1379, 1454, 1531, 1610, 1691, 1774, 1859, 1946, 2035, 2126, 2219, 2314, 2411, 2510
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OFFSET
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1,1
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COMMENTS
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Conjecture: n^2 + 10 != x^k for all n,x, and k>1.
The conjecture is true: See Cohn. - James Rayman, Feb 14 2023
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LINKS
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FORMULA
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Sum_{n>=0} 1/a(n) = (1 + sqrt(10)*Pi*coth(sqrt(10)*Pi))/20.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(10)*Pi*cosech(sqrt(10)*Pi))/20. (End)
Product_{n>=0} (1 - 1/a(n)) = (3/sqrt(10))*sinh(3*Pi)/sinh(sqrt(10)*Pi).
Product_{n>=0} (1 + 1/a(n)) = sqrt(11/10)*sinh(sqrt(11)*Pi)/sinh(sqrt(10)*Pi). (End)
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MATHEMATICA
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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