A071524 Determinant of n X n matrix defined by m(i,j)=1 if i^2+j^2 is a prime, m(i,j)=0 otherwise.

1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 16, 25, -25, -100, 1, 81, -16, -36, 0, 1764, -3136, -196, 324, 16, -225, -1764, 1521, 9, -3969, -4356, 4761, 9, -1225, -19881, 5041, 156816, -312481, -167281, 219024, 3600, -186624, -158404, 5541316, 3020644, -19554084, -1350244, 198810000

Offset

1,20

Comments

Terms are also perfect squares.

Conjecture: a(n) = 0 for no n > 28. - Zhi-Wei Sun, Aug 26 2013

General conjecture: Let m be any nonnegative integer, and let a(m,n) be the n X n determinant with (i,j)-entry equal to 1 or 0 according as i^{2^m}+j^{2^m} is prime or not. Then a(m,n) is nonzero for large n. (It can be proved that (-1)^(n*(n-1)/2}*a(m,n) is always a square, see the comments in A228591.) - Zhi-Wei Sun, Aug 26-27 2013

Links

Table of n, a(n) for n=1..56.

Mathematica

a[n_]:=a[n]=Det[Table[If[PrimeQ[i^2+j^2]==True, 1, 0], {i, 1, n}, {j, 1, n}]]; Table[a[n], {n, 1, 30}] (* Zhi-Wei Sun, Aug 26 2013 *)
Table[Det[Table[If[PrimeQ[a^2+b^2], 1, 0], {a, n}, {b, n}]], {n, 60}] (* Harvey P. Dale, May 31 2019 *)

Prog

(PARI) for(n=1, 60, print1(((matdet(matrix(n, n, i, j, isprime(i^2+j^2))))), ", "))

Crossrefs

Cf. A069191, A228591, A228552, A228557, A228559, A228561, A228574, A228578.

Sequence in context: A087622 A170985 A202335 * A334392 A227651 A348320

Adjacent sequences: A071521 A071522 A071523 * A071525 A071526 A071527

Keyword

easy,sign

Author

Benoit Cloitre, Jun 02 2002

Status

approved