A324795 a(n) = 2*p(n)*p(n+2) - p(n+1)^2 where p(k) = k-th prime.

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

Author

N. J. A. Sloane, Sep 10 2019

Keywords

• nonn

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

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A056221 (if leading coefficient 2 is changed to 1), A327447 or A309487 (if 2 is changed to 4).

Programs

Mathematica

With[{p = Prime[Range[50]]}, 2 * p[[1;;-3]] * p[[3;;-1]] - p[[2;;-2]]^2] (* Amiram Eldar, Apr 25 2024 *)