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%I #8 Apr 12 2023 11:08:21
%S 1,1,1,3,8,31,87,340,959,3751,10581,41396
%N Least numbers, starting (1,1,1), such that determinants of continuous blocks of 4 form an increasing sequence of primes (A119839).
%C 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, ...
%F 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)}.
%F 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.
%e a(6) = 87 because of the prime determinant 13 = | 3 8|
%e |31 87|.
%Y Cf. A000040, A119839.
%K nonn,more,uned
%O 0,4
%A _Jonathan Vos Post_, May 25 2006
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