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Search: id:A114454
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| A114454 |
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Numbers n such that the n-th hexagonal number is a 3-almost prime. |
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1
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| 4, 5, 6, 9, 10, 11, 13, 15, 17, 21, 22, 29, 34, 43, 47, 49, 51, 55, 57, 61, 67, 69, 71, 73, 82, 87, 89, 91, 101, 103, 106, 107, 109, 115, 121, 127, 129, 141, 142, 151, 159, 166, 169, 177, 181, 187, 191, 197, 201, 205, 217, 223, 227, 241, 251, 262, 269, 274, 277, 283
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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There are no prime hexagonal numbers. The n-th Hexagonal number A000384(n) = n*(2*n-1) is semiprime iff both n and 2*n-1 are prime iff A000384(n) is an element of A001358 iff n is an element of A005382.
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LINKS
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Eric Weisstein's World of Mathematics, Hexagonal Number.
Eric Weisstein's World of Mathematics, Almost Prime.
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FORMULA
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n such that hexagonal number A000384(n) is an element of A014612. n such that A001222(A000384(n)) = 3. n such that A001222(n*(2*n-1)) = 3.
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EXAMPLE
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a(1) = 4 because HexagonalNumber(4) = H(4) = 4*(2*4-1) = 28 = 2^2 * 7 is a 3-almost prime.
a(2) = 5 because H(5) = 5*(2*5-1) = 45 = 3^2 * 5 is a 3-almost prime.
a(3) = 6 because H(6) = 6*(2*6-1) = 66 = 2 * 3 * 11 is a 3-almost prime.
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MAPLE
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A000384 := proc(n) n*(2*n-1) ; end: isA014612 := proc(n) option remember ; RETURN( numtheory[bigomega](n) = 3) ; end: for n from 1 to 400 do if isA014612(A000384(n)) then printf("%d, ", n) ; fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 27 2009]
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CROSSREFS
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Cf. A000384, A001222, A014612.
Sequence in context: A049466 A139546 A029776 this_sequence A008854 A062726 A159629
Adjacent sequences: A114451 A114452 A114453 this_sequence A114455 A114456 A114457
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 14 2006
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EXTENSIONS
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151 to 177 inserted and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 27 2009
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