OFFSET
1,29
COMMENTS
Conjecture: a(n) is nonzero for each n > 28.
This implies that there are infinitely many primes p with 4*p^2 + 1 also prime. Note also that (-1)^{n*(n-1)/2}*a(n) is always a square in view of the comments in A228591.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..300
EXAMPLE
a(1) = 1 since 1 + 1 = 2 and 4*2^2 + 1 = 17 are both prime.
MATHEMATICA
a[n_]:=a[n]=Det[Table[If[PrimeQ[i+j]==True&&PrimeQ[4(i+j)^2+1]==True, 1, 0], {i, 1, n}, {j, 1, n}]]
Table[a[n], {n, 1, 30}]
CROSSREFS
KEYWORD
sign
AUTHOR
Zhi-Wei Sun, Aug 25 2013
STATUS
approved