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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, 1, 3, 8, 31, 87, 340, 959, 3751, 10581, 41396 (list; graph; refs; listen; history; text; internal format)
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 the of the prime determinant 13 =

|.3..8|

|31.87|.

CROSSREFS

Cf. A000040, A119839.

Sequence in context: A145776 A066165 A323775 * A148889 A148890 A148891

Adjacent sequences: A119835 A119836 A119837 * A119839 A119840 A119841

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, May 25 2006

STATUS

approved

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Last modified February 4 04:43 EST 2023. Contains 360046 sequences. (Running on oeis4.)