cp's OEIS Frontend

A118873 Determinant of n-th continuous block of 4 consecutive squares of primes.

%I A118873 #16 Jan 25 2021 08:59:36
%S A118873 -29,-136,-1704,-6288,-5160,-14928,52080,-97968,-84000,98112,-524400,
%T A118873 -84048,637488,231288,-1558440,-343200,844152,-2799840,1152360,
%U A118873 1469160,-783240,4153800,-4254000,-11947320,-498768,-264360,-559248,32952432,-2061360,-37128408,-10466400,18355512
%N A118873 Determinant of n-th continuous block of 4 consecutive squares of primes.
%C A118873 Quadratic analog of A117301 Determinants of 2 X 2 matrices of continuous blocks of 4 consecutive primes. See also: A001248 Squares of primes. The terminology "continuous" is used to distinguish from "discrete" which would be block 1: 4, 9, 25, 49; block 2: 121, 169, 289, 361; and so forth. Through n = 10^6, the number of negative values a(n) in this sequence appears to be consistently larger than the number of positive values.
%F A118873 a(n) = prime(n)^2*prime(n+3)^2 - prime(n+1)^2*prime(n+2)^2.
%e A118873 a(1) = -29 =
%e A118873   | 4   9|
%e A118873   |25  49|.
%p A118873 a:= n-> LinearAlgebra[Determinant](Matrix(2, (i,j)-> ithprime(n+2*i-3+j)^2)):
%p A118873 seq(a(n), n=1..32);  # _Alois P. Heinz_, Jan 25 2021
%t A118873 m = 32; p = Prime[Range[m + 3]]^2; Table[Det @ Partition[p[[n ;; n + 3]], 2], {n, 1, m}] (* _Amiram Eldar_, Jan 25 2021 *)
%o A118873 (PARI) a(n) = prime(n)^2*prime(n+3)^2 - prime(n+1)^2*prime(n+2)^2; \\ _Michel Marcus_, Jan 25 2021
%Y A118873 Cf. A000040, A001248, A117301.
%K A118873 easy,sign
%O A118873 1,1
%A A118873 _Jonathan Vos Post_, May 24 2006