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 A240986 Determinants of n X n matrices of sets of distinct primes selected by increasing prime gaps (see comments). 1
 3, 6, -36, -216, 1296, -5184, -145152, -3856896, -170325504, -6133211136, 1094593056768, 26742290558976, -497681937801216, -14357497419546624, 657148066947072000, 12008320398059765760, 1322255096225695531008, 70546799432003423698944, -6537119853797882157072384, -27940593871362459110473728 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Let P = {3,5,7,11,...} be the sequence of odd primes and let P(k) = {prime in P: (prime+2k) is in P} (although set builder notation is used for P(k) we will still assume that P(k) is a sequence). Let M(n) be the n X n matrix where row 1 is the first n elements from P(1), row 2 is the first n elements from P(2), and in general row j is the first n elements from P(j). This sequence is the sequence of determinants for M(1), M(2), M(3), M(4), ..., M(9). LINKS Samuel J. Erickson, Python Code Sachin Joglekar, Determinant of matrix of any order (Python) EXAMPLE For the first element of the sequence we find the determinant of the matrix [[3,5],[3,7]], where [3,5] is row 1 and [3,7] is row 2. These numbers are there because in row 1 we are looking at the primes where we can add 2 to get another prime; 3+2 is prime and so is 5+2, so they go in row 1. Similarly, for the second row we get [3,7] because these are the first primes such that when 4 is added we get a prime: 3+4 and 7+4 are both prime, so they go in row 2. For the second entry in the sequence we take the determinant of [[3,5,11],[3,7,13],[5,7,11]]; the reason we get [5,7,11] in the third row is because 5 is the first prime where 5+6 is prime, 7 is second prime where 7+6 is prime, and 11 is the third prime where 11+6 is prime. PROG (Python) See link for code. (PARI) a(n) = {my(m=matrix(n, n), j); for (i=1, n, j = 1; forprime(p=2, , if (isprime(p+2*i), m[i, j] = p; j++); if (j > n, break); ); ); matdet(m); } \\ Michel Marcus, May 04 2019 CROSSREFS Cf. A001359, A023200, A023201, A023202, A023203. Sequence in context: A068084 A003674 A211895 * A120595 A048642 A264702 Adjacent sequences:  A240983 A240984 A240985 * A240987 A240988 A240989 KEYWORD sign,more AUTHOR Samuel J. Erickson, Aug 06 2014 EXTENSIONS Offset 1 and more terms from Michel Marcus, May 04 2019 STATUS approved

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Last modified October 15 01:40 EDT 2019. Contains 328025 sequences. (Running on oeis4.)