

A228623


Determinant of the n X n matrix with (i,j)entry (i,j = 0,...,n1) equal to 1 or 0 according as n + i  j and n  i + j are both prime or not.


3



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
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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

ZhiWei 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+ji]==True&&PrimeQ[n+ij]==True, 1, 0], {i, 0, n1}, {j, 0, n1}]]
Table[a[n], {n, 1, 20}]


CROSSREFS

Cf. A002372, A228591, A228615, A228616, A228557, A228559.
Sequence in context: A049759 A265421 A137252 * A036875 A036877 A049763
Adjacent sequences: A228620 A228621 A228622 * A228624 A228625 A228626


KEYWORD

sign


AUTHOR

ZhiWei Sun, Aug 27 2013


STATUS

approved



