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Search: id:A113530
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| A113530 |
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Semiprimes in sixth spoke of a hexagonal spiral (A003215). Semiprime hex (or centered hexagonal) numbers. |
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+0
2
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| 91, 169, 217, 469, 721, 817, 1027, 1141, 1261, 1387, 2611, 2977, 3781, 3997, 4681, 5677, 5941, 6487, 6769, 7651, 7957, 8587, 9577, 10981, 11347, 12481, 12871, 14077, 14491, 15769, 16207, 17557, 18019, 18961, 20419, 20917, 21421, 22969, 24031
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(1) = 91 because A003215(5) = (5+1)^3 - 5^3 = 91 = 7 * 13 is semiprime. A003215(1) = 7, A003215(2) = 19, A003215(3) = 37, A003215(4) = 61, are not in the sequence, as they are primes. a(7) = 121 because A003215(7) = (7+1)^3 - 7^3 = 169 = 13^2 is semiprime; the two prime factors need not be distinct. A003215(59) = (59+1)^3 - 59^3 = 10621 = 13 * 19 * 43 is not in the sequence, as it is a 3-almost prime [whose prime factors have the same number of digits, a so-called 3-brilliant number, as is (70+1)^3 - 70^3 = 14911 = 13 * 31 * 37; similarly, (87+1)^3 - 87^3 = 22969 = 103 * 223 is called 2-brilliant]. A003215(100) = (100+1)^3 - 100^3 = 30301 = 157 * 193 which is semiprime.
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LINKS
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Eric Weisstein's World of Mathematics, Hex Number.
H. Bottomley, Spokes of a hexagonal spiral.
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FORMULA
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{a(n)} = {3*n^2 + 3*n + 1 iff semiprime}. {a(n)} = {n+1)^3 - n^3 iff semiprime}. {a(n)} = A003215 INTERSECT A001358.
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CROSSREFS
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Cf. A001358, A003215.
Sequence in context: A088983 A045934 A051347 this_sequence A119148 A037998 A063367
Adjacent sequences: A113527 A113528 A113529 this_sequence A113531 A113532 A113533
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Jan 12 2006
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