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
KEYWORD
nonn
AUTHOR
Freimut Marschner, Jul 10 2014
STATUS
approved