A298903 Determinant of n X n matrix whose elements are m(i,j) = prime(i+j)-prime(i).
1, 1, -2, 4, 48, 192, -1216, 4672, 120704, 115712, -1717760, -4103168, 10545152, 8527872, -520617984, -8178925568, 97259454464, -1335459315712, -19462172966912, -360902649708544, -1350652745744384, 74944810429972480, -12488535009247887360, -107854339949694287872, 84090212651516146221056
Offset: 0
Keywords
Examples
For n=1:
|prime(2) - prime(1)| = |3 - 2| = |1| = 1,
then a(1) = 1.
For n=2:
|prime(2)-prime(1) prime(3)-prime(1)| = |3-2 5-2| = |1 3|= -2,
|prime(3)-prime(2) prime(4)-prime(2)| |5-3 7-3| |2 4|
then a(2) = -2.
Programs
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Maple
with(LinearAlgebra): a:= n-> Determinant(Matrix(n, (i,j)-> ithprime(i+j)-ithprime(i))): seq(a(n), n=0..25); # Alois P. Heinz, Jan 28 2018
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Mathematica
b[n_]:=Table[(Prime[i+j]-Prime[i]),{i,1,n},{j,1,n}]; Table[Det[b[n]],{n,1,24}] -
PARI
a(n) = matdet(matrix(n, n, i, j, prime(i+j)-prime(i))); \\ Michel Marcus, Jan 28 2018