A245035 a(n) = (prime(n) - 7)^2 * (4*prime(n) - 1).

175, 176, 76, 0, 688, 1836, 6700, 10800, 23296, 55660, 70848, 132300, 188428, 221616, 299200, 446476, 635440, 708588, 961200, 1159168, 1267596, 1632960, 1911856, 2387020, 3134700, 3560908, 3787776, 4270000, 4525740, 5067436, 7300800, 8041648, 9244300

Offset

1,1

Comments

The discriminant D of the Cardano Tartaglia equation x^3 + p*x + q = 0 is written -D = 27*q^2 + 4*p^3. Let q = p = prime(n) - 7 then -D = 27*(prime(n) - 7)^2 + 4*(prime(n) - 7)^3 = (prime(n)-7)^2 * ( 4*(prime(n) - 7) + 27 ) = (prime(n) - 7)^2 * (4* prime(n) - 4*7 + 27) = (7 - prime(n))^2 * (4* prime(n) - 1) = a(n).

Links

Freimut Marschner, Table of n, a(n) for n = 1..6320

Formula

a(n) = 27*(prime(n) - 7)^2 + 4*(prime(n) - 7)^3.

Example

a(1) = (2 - 7)^2*(4*2 - 1) = 25*7 = 175.
a(4) = (7 - 7)^2*(4*7 - 1) = 0.

Mathematica

(#-7)^2 (4#-1)&/@Prime[Range[40]] (* Harvey P. Dale, Jul 19 2022 *)

Prog

(Magma) [4*p^3-57*p^2+210*p-49: p in PrimesUpTo(200)]; // Bruno Berselli, Jul 31 2014

Crossrefs

Cf. A000040 (prime(n)), A001248 (prime(n)^2), A030078 (prime(n)^3).

Sequence in context: A252717 A187425 A186218 * A102538 A045145 A351720

Adjacent sequences: A245032 A245033 A245034 * A245036 A245037 A245038

Keyword

nonn

Author

Freimut Marschner, Jul 10 2014

Status

approved