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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. 2
0, -1, 12, -80, 1152, -5632, 61440, -278528, 2752512, -42467328, 182452224, -2642411520, 23555211264, -99052683264, 869730877440, -11828339933184, 158638912045056, -656820758642688, 8683393080360960, -73742045851680768 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

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

EXAMPLE

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

MATHEMATICA

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

Table[a[n], {n, 1, 20}]

CROSSREFS

Cf. A000040, A185645.

Sequence in context: A258591 A058962 A203486 * A277783 A009500 A012195

Adjacent sequences:  A187008 A187009 A187010 * A187012 A187013 A187014

KEYWORD

sign

AUTHOR

Zhi-Wei Sun, Aug 30 2013

STATUS

approved

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Last modified January 23 20:39 EST 2021. Contains 340386 sequences. (Running on oeis4.)