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A324795
a(n) = 2*p(n)*p(n+2) - p(n+1)^2 where p(k) = k-th prime.
2
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
OFFSET
1,1
COMMENTS
Theorem: a(n) > 0. Proof: Use p(n+1) <= 2 p(n)^2 for n > 4. (See Sándor et al.) QED
REFERENCES
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.
LINKS
MATHEMATICA
With[{p = Prime[Range[50]]}, 2 * p[[1;; -3]] * p[[3;; -1]] - p[[2;; -2]]^2] (* Amiram Eldar, Apr 25 2024 *)
CROSSREFS
Cf. A056221 (if leading coefficient 2 is changed to 1), A327447 or A309487 (if 2 is changed to 4).
Sequence in context: A377856 A242244 A228031 * A250716 A244853 A102870
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 10 2019
STATUS
approved