A228623 Determinant of the n X n matrix with (i,j)-entry (i,j = 0,...,n-1) equal to 1 or 0 according as n + i - j and n - i + j are both prime or not.

0, 1, 1, 1, 0, -1, 0, 0, 0, -4, -1, 0, 0, 0, -6, 0, 0, -144, 0, 0, 0, -1, 168, 1024, 420, 0, 0, 0, -1, -9801, 0, 144, 0, 0, 3072, 7056, 0, 0, -42346434, 0, 0, -331776, 0, 0, 36528128, -104976, 96545145, 0, 34665386, -62500, 2826240, 2025, 0, -23174596, 0, 0, 255578880, -4, -3, 990172089

Offset

1,10

Comments

Conjecture: a(n) is nonzero if n is odd and greater than 120.

This implies Goldbach's conjecture for even numbers of the form 4*k + 2.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..400

Example

a(1) = 0 since 1 + 0 - 0 = 1 is not a prime.

Mathematica

a[n_]:=Det[Table[If[PrimeQ[n+j-i]==True&&PrimeQ[n+i-j]==True, 1, 0], {i, 0, n-1}, {j, 0, n-1}]]
Table[a[n], {n, 1, 20}]

Crossrefs

Cf. A002372, A228591, A228615, A228616, A228557, A228559.

Sequence in context: A355829 A265421 A137252 * A036875 A036877 A379967

Adjacent sequences: A228620 A228621 A228622 * A228624 A228625 A228626

Keyword

sign

Author

Zhi-Wei Sun, Aug 27 2013

Status

approved