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A114517
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Numbers n such that n-th heptagonal number is semiprime.
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0
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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, 158, 166, 173, 178, 194, 197, 218, 229, 241, 257, 262, 274, 277, 281, 298, 314, 326, 334, 353, 358, 382, 389, 397, 398, 409, 421, 454, 458, 461, 521, 538
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OFFSET
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1,1
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COMMENTS
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Hep(2) = 7 is the only prime heptagonal number.
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LINKS
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Table of n, a(n) for n=1..56.
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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MATHEMATICA
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Select[Range[700], PrimeOmega[(#(5#-3))/2]==2&] (* From Harvey P. Dale, Jul 24 2011 *)
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CROSSREFS
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Cf. A000040, A000566, A001222, A001358, A099153.
Sequence in context: A058335 A222353 A094415 * A116930 A073119 A002257
Adjacent sequences: A114514 A114515 A114516 * 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, Feb 15 2006
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EXTENSIONS
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More terms from Harvey P. Dale, Jul 24 2011
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STATUS
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approved
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