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A119838
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Least numbers, starting (1,1,1), such that determinants of continuous blocks of 4 form an increasing sequence of primes (A119839).
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1
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1, 1, 1, 3, 8, 31, 87, 340, 959, 3751, 10581, 41396
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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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, ...
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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.
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EXAMPLE
| a(6) = 87 because the of the prime determinant 13 =
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|31.87|.
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CROSSREFS
| Cf. A000040, A119839.
Sequence in context: A066304 A145776 A066165 * A148889 A148890 A148891
Adjacent sequences: A119835 A119836 A119837 * A119839 A119840 A119841
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), May 25 2006
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