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 A069191 Determinant of n X n matrix defined by m(i,j)=1 if i+j is a prime, m(i,j)=0 otherwise. 16
 1, -1, -1, 0, 1, -1, -4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, -9, -25, 121, 64, -576, -2304, 3600, 3136, -256, -144, 961, 24025, -47089, -345744, 1317904, 107584, -26896, -30976, 17424, 30976, -156025, -76729, 485809, 478864, -36481, -837225, 5776, 517198564, -15791440896, -16404230241, 45746793225 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS Abs(a(n)) is always a perfect square. A general result for Hankel determinants: Given any sequence a(0),a(1),... of numbers, let the n X n Hankel matrix A[i,j]=x if i=j=0, 0 if i+j even and a(((i+j)-1)/2) otherwise where 0<=i,j -lambda(2) > lambda(3) > -lambda(4) > .... > (-1)^n*lambda(n) > 0. - Zhi-Wei Sun, Aug 25 2013 That (-1)^(n(n-1)/2)*a(n) is a perfect square is a special case of a general theorem mentioned in A228591. - Zhi-Wei Sun, Aug 25 2013 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..500 MATHEMATICA f[n_] := Det[ Table[ If[ PrimeQ[i + j], 1, 0], {i, 1, n}, {j, 1, n}]]; Table[ f[n], {n, 1, 45}] CROSSREFS Cf. A073364. Sequence in context: A344407 A197243 A175372 * A175362 A189973 A282866 Adjacent sequences: A069188 A069189 A069190 * A069192 A069193 A069194 KEYWORD sign AUTHOR Santi Spadaro, Apr 19 2002 STATUS approved

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Last modified February 3 18:43 EST 2023. Contains 360044 sequences. (Running on oeis4.)