A245034 a(n) = prime(n)^2 - 4*prime(n).

5, 21, 77, 117, 221, 285, 437, 725, 837, 1221, 1517, 1677, 2021, 2597, 3245, 3477, 4221, 4757, 5037, 5925, 6557, 7565, 9021, 9797, 10197, 11021, 11445, 12317, 15621, 16637, 18221, 18765, 21605, 22197, 24021, 25917, 27221, 29237, 31325, 32037, 35717, 36477, 38021, 38805, 43677, 48837

Offset

3,1

Comments

The discriminant D of the quadratic equation n^2 + p*n + q = 0 is D = p^2 - 4*q. Let p = q = prime(n) then a(n) = D. 0 < n <= 2, D < 0, is the « casus irreducibilis ». So the offset is set to n = 3 to get positive integers as real solutions. Remark: a(0) is not defined, a(1) = -4, a(2) = -3.

Links

Jens Kruse Andersen, Table of n, a(n) for n = 3..10000

Formula

a(n) = prime(n)^2 - 4*prime(n) = A001248(n) - 4*A000040(n), n > 2.

Example

For n = 6, prime(6) = 13, so a(6) = 13^2 - 4*13 = 169 - 52 = 117.

Maple

A245034:=n->ithprime(n)^2-4*ithprime(n): seq(A245034(n), n=3..50); # Wesley Ivan Hurt, Jul 12 2014

Mathematica

Table[Prime[n]^2 - 4 Prime[n], {n, 3, 50}] (* Wesley Ivan Hurt, Jul 12 2014 *)
#^2-4#&/@Prime[Range[3, 50]] (* Harvey P. Dale, Apr 03 2022 *)

Crossrefs

Cf. A028347 (n^2 - 4*n), A000290 (squares n^2), A000040 (prime(n)), A001248 (prime(n)^2).

Sequence in context: A272452 A271088 A271694 * A126645 A026329 A014533

Adjacent sequences: A245031 A245032 A245033 * A245035 A245036 A245037

Keyword

nonn,easy

Author

Freimut Marschner, Jul 10 2014

Status

approved