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Search: id:A118781
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| A118781 |
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Determinants of 3 X 3 matrices of continuous blocks of 9 consecutive semiprimes. |
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+0
2
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| -196, 272, -251, 149, -423, 909, -408, -452, 958, -123, -112, -460, 84, -271, -187, -162, 63, 7, 101, -483, -133, 205, -860, -46, 339, 1178, 848, 366, 1084, 719, -384, 334, -2736, -984, -1912, 214, 34, 40, -1735, -60, 64, -2263, -3468, 5795, 69, 132, 3007, 256, 2130, 3428
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Semiprime analogue of A117330 Determinants of 3 X 3 matrices of continuous blocks of 9 consecutive primes. The terminology "continuous" is used to distinguish from "discrete" which would be (in this 3 X 3 semiprime case) block 1: 4, 6, 9, 10, 14, 15, 21, 22, 25; block 2: 26, 33, 34, 35, 38, 39, 46, 49, 51; and so forth.
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FORMULA
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a(n) = s(n)*s(n+4)*s(n+8) - s(n)*s(n+5)*s(n+7) - s(n+1)*s(n+3)*s(n+8) + s(n+1)*s(n+5)*s(n+6) + s(n+2)*s(n+3)*s(n+7) - s(n+2)*s(n+4)*s(n+6) where s(n) = A001358(n) is the n-th semiprime.
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EXAMPLE
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a(1) = -196 because the determinant of the first continuous block of 9 semiprimes is:
| 4. 6. 9.|
|10. 14. 15.|
|21. 22. 25.|.
a(9) = 958 because the determinant of the 9th continuous block of 9 semiprimes is:
|25. 26. 33.|
|34. 35. 38.|
|39. 46. 49.|.
a(50) = 3428 because the determinant of the 50th continuous block of 9 semiprimes is:
|146. 155. 158.|
|159. 161. 166.|
|169. 177. 178.|.
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CROSSREFS
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Cf. A001358, A067276, A117301, A118713.
Sequence in context: A084232 A077594 A044870 this_sequence A119667 A023108 A092231
Adjacent sequences: A118778 A118779 A118780 this_sequence A118782 A118783 A118784
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KEYWORD
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easy,sign
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), May 22 2006
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