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A324795
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a(n) = 2*p(n)*p(n+2) - p(n+1)^2 where p(k) = k-th prime.
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2
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11, 17, 61, 61, 205, 205, 421, 573, 585, 1185, 1173, 1501, 2005, 2349, 2737, 2985, 4185, 4173, 4741, 5889, 5877, 7173, 8181, 8569, 9781, 11005, 11005, 12301, 14917, 13477, 17637, 17649, 21505, 19777, 23985, 24577, 25869, 28509, 29857, 30585, 35617
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OFFSET
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1,1
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COMMENTS
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Theorem: a(n) > 0. Proof: Use p(n+1) <= 2 p(n)^2 for n > 4. (See Sándor et al.) QED
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REFERENCES
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József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter VII, p. 247, section VII.18.b.
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LINKS
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MATHEMATICA
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With[{p = Prime[Range[50]]}, 2 * p[[1;; -3]] * p[[3;; -1]] - p[[2;; -2]]^2] (* Amiram Eldar, Apr 25 2024 *)
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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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