A187011 Determinant of the n X n matrix with (i,j)-entry equal to |p_i-p_j|, where p_k denotes the k-th prime.

0, -1, 12, -80, 1152, -5632, 61440, -278528, 2752512, -42467328, 182452224, -2642411520, 23555211264, -99052683264, 869730877440, -11828339933184, 158638912045056, -656820758642688, 8683393080360960, -73742045851680768

Offset: 1

Author

Zhi-Wei Sun, Aug 30 2013

Keywords

• sign

Comments

Conjecture: (-1)^(n-1)*a(n) > 0 for all n > 1, and |a(n)|^{1/n} tends to the infinity.

Examples

			a(1) = 0 since p_1 - p_1 = 2 - 2 = 0.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A000040, A185645.

Programs

Mathematica

a[n_]:=Det[Table[Abs[Prime[i]-Prime[j]],{i,1,n},{j,1,n}]]
Table[a[n],{n,1,20}]