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

%I #30 Apr 03 2022 15:16:25

%S 5,21,77,117,221,285,437,725,837,1221,1517,1677,2021,2597,3245,3477,

%T 4221,4757,5037,5925,6557,7565,9021,9797,10197,11021,11445,12317,

%U 15621,16637,18221,18765,21605,22197,24021,25917,27221,29237,31325,32037,35717,36477,38021,38805,43677,48837

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

%C 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.

%H Jens Kruse Andersen, <a href="/A245034/b245034.txt">Table of n, a(n) for n = 3..10000</a>

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

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

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

%t Table[Prime[n]^2 - 4 Prime[n], {n, 3, 50}] (* _Wesley Ivan Hurt_, Jul 12 2014 *)

%t #^2-4#&/@Prime[Range[3,50]] (* _Harvey P. Dale_, Apr 03 2022 *)

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

%K nonn,easy

%O 3,1

%A _Freimut Marschner_, Jul 10 2014