cp's OEIS Frontend

A298903 Determinant of n X n matrix whose elements are m(i,j) = prime(i+j)-prime(i).

%I A298903 #12 Jan 29 2018 09:59:54
%S A298903 1,1,-2,4,48,192,-1216,4672,120704,115712,-1717760,-4103168,10545152,
%T A298903 8527872,-520617984,-8178925568,97259454464,-1335459315712,
%U A298903 -19462172966912,-360902649708544,-1350652745744384,74944810429972480,-12488535009247887360,-107854339949694287872,84090212651516146221056
%N A298903 Determinant of n X n matrix whose elements are m(i,j) = prime(i+j)-prime(i).
%e A298903 For n=1:
%e A298903          |prime(2) - prime(1)| = |3 - 2| = |1| = 1,
%e A298903 then a(1) = 1.
%e A298903 For n=2:
%e A298903          |prime(2)-prime(1) prime(3)-prime(1)| = |3-2 5-2| = |1 3|= -2,
%e A298903          |prime(3)-prime(2) prime(4)-prime(2)|   |5-3 7-3|   |2 4|
%e A298903 then a(2) = -2.
%p A298903 with(LinearAlgebra):
%p A298903 a:= n-> Determinant(Matrix(n, (i,j)-> ithprime(i+j)-ithprime(i))):
%p A298903 seq(a(n), n=0..25);  # _Alois P. Heinz_, Jan 28 2018
%t A298903 b[n_]:=Table[(Prime[i+j]-Prime[i]),{i,1,n},{j,1,n}];
%t A298903 Table[Det[b[n]],{n,1,24}]
%o A298903 (PARI) a(n) = matdet(matrix(n, n, i, j, prime(i+j)-prime(i))); \\ _Michel Marcus_, Jan 28 2018
%Y A298903 Cf. A187011, A298883.
%K A298903 sign
%O A298903 0,3
%A A298903 _Andres Cicuttin_, Jan 28 2018