A119838 Least numbers, starting (1,1,1), such that determinants of continuous blocks of 4 form an increasing sequence of primes (A119839).

1, 1, 1, 3, 8, 31, 87, 340, 959, 3751, 10581, 41396

Offset

0,4

Comments

In calculating this sequence, some backtracking may be needed to ensure that the sequence is unbounded. For instance, one makes the preliminary assignment a(4) = 6, since determinant[1,1,3,6] = 3, a prime greater than the previous determinant prime in A119839: 2. Then one computes a(5) = 23, giving determinant[1,3,6,23] = 5. However, the sequence hits a wall here, as any putative a(6) gives a composite determinant divisible by 3, hence we must backtrack and reassign a(4) = 8. The associated sequence of primes A119839 = 2, 5, 7, 13, 23, 149, 277, 331, 9433, ...

Links

Table of n, a(n) for n=0..11.

Formula

a(0) = a(1) = a(2) = 1; for n>2: a(n) = min{k such that k*a(n-3) - a(n-1)*a(n-2) is prime p, p>A119839(n-1)}.

Determinant [a(n-3),a(n-2),a(n-1),a(n)] = a(n)*a(n-3) - a(n-1)*a(n-2) is a prime greater than any previous prime in the associated sequence of primes A119839.

Example

a(6) = 87 because of the prime determinant 13 = | 3  8|
                                                |31 87|.

Crossrefs

Cf. A000040, A119839.

Sequence in context: A066165 A323775 A360605 * A148889 A148890 A148891

Adjacent sequences: A119835 A119836 A119837 * A119839 A119840 A119841

Keyword

nonn,more,uned

Author

Jonathan Vos Post, May 25 2006

Status

approved