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Search: id:A114517
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| A114517 |
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Numbers n such that n-th heptagonal number is semiprime. |
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1
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| 4, 5, 10, 13, 14, 17, 22, 26, 29, 34, 41, 46, 53, 61, 62, 73, 74, 94, 97, 101, 109, 113, 118, 122, 146
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Hep(2) = 7 is the only prime heptagonal number.
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LINKS
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Eric Weisstein's World of Mathematics, Heptagonal Number.
Eric Weisstein's World of Mathematics, Semiprime.
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FORMULA
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n such that Hep(n) = n*(5*n-3)/2 is semiprime. n such that A000566(n) is an element of A001358. n such that A001222(A000566(n)) = 2. n such that A001222(n*(5*n-3)/2) = 2. n such that [n/2 prime and 5*n-3 prime] or [n prime and (5*n-3)/2 prime].
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EXAMPLE
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a(1) = 4 because Hep(4) = 4*(5*4-3)/2 = 34 = 2 * 17 is semiprime.
a(2) = 5 because Hep(5) = 5*(5*5-3)/2 = 55 = 5 * 11 is semiprime.
a(10) = 34 because Hep(34) = 2839 = 17 * 167 is semiprime, and this is also the first iterated heptagonal semiprime Hep(34) = Hep(Hep(4)).
a(20) = 101 because Hep(101) = 25351 = 101 * 251 is semiprime [and brilliant].
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CROSSREFS
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Cf. A000040, A000566, A001222, A001358, A099153.
Sequence in context: A050039 A058335 A094415 this_sequence A116930 A073119 A002257
Adjacent sequences: A114514 A114515 A114516 this_sequence A114518 A114519 A114520
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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), Feb 15 2006
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