1,1

The first column contains the first n primes in increasing order, the second column contains the next n primes in increasing order, etc. Equivalently, first row contains first n primes in increasing order, second row contains next n primes in increasing order, etc. Sequences of determinants of matrices specifically containing primes include A024356 (Hankel matrix), A067549 (first n primes on diagonal, other elements 1), A066933 (cyclic permutations of first n primes in each row) and A067551 (first n primes on diagonal, other elements 0).

a(3) = -78 because det[[2,7,17],[3,11,19],[5,13,23]] = -78 (= det[[2,3,5],[7,11,13],[17,19,23]], the determinant of the transpose.).

Table[ Det[ Partition[ Array[Prime, n^2], n]], {n, 19}] (from Robert G. Wilson v (rgwv(at)rgwv.com), May 26 2006)

(PARI) for(n=1, 20, k=0; m=matrix(n, n, x, y, prime(k=k+1)); print(matdet(m))) (The matrix initialization command above fills columns first: Variables (such as) x and y take on values 1 through n for rows and columns, respectively, with x changing more rapidly, and they must be specified even though the 5th argument is not an explicit function of them here.).

Cf. A024356, A067549, A066933, A067551.

Cf. A119894, A118770, A118772, A118779.

Sequence in context: A092650 A104024 A096681 this_sequence A118580 A118558 A095837

Adjacent sequences: A067273 A067274 A067275 this_sequence A067277 A067278 A067279

easy,sign

Rick L. Shepherd (rshepherd2(AT)hotmail.com), Feb 21 2002