

A228616


Determinant of the n X n matrix with (i,j)entry equal to 1 or 0 according as 2*(i + j)  1 is prime or not.


9



1, 0, 1, 2, 0, 0, 0, 2, 3, 11, 24, 60, 16, 31, 217, 1148, 164, 132, 395, 697, 191, 76, 125664, 213885, 171654, 114902, 353497, 388325, 1738118, 222898, 248633, 382075, 1637075, 21100, 4049068, 189147708, 279083383, 472023163, 19063401, 6718578823
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OFFSET

1,4


COMMENTS

Conjecture: a(n) is nonzero for any n > 7.
Clearly this conjecture implies that there are infinitely many primes.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..250


EXAMPLE

a(1) = 1 since 2*(1 + 1)  1 = 3 is a prime.


MATHEMATICA

a[n_]:=a[n]=Det[Table[If[PrimeQ[2(i+j)1], 1, 0], {i, 1, n}, {j, 1, n}]]
Table[a[n], {n, 1, 40}]


CROSSREFS

Cf. A000040, A069191, A228615, A228591.
Sequence in context: A063958 A126164 A145007 * A151670 A153587 A059286
Adjacent sequences: A228613 A228614 A228615 * A228617 A228618 A228619


KEYWORD

sign


AUTHOR

ZhiWei Sun, Aug 27 2013


STATUS

approved



