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Search: id:A106483
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| 2, 3, 7, 11, 13, 17, 41, 43, 59, 73, 109, 113, 127, 137, 157, 179, 181, 197, 199, 211, 251, 263, 277, 293, 311, 353, 367, 379, 409, 419, 433, 487, 563, 571, 577, 617, 619, 659, 701, 739, 743, 757, 797, 811, 827, 829, 839, 857, 937, 941, 1009, 1039, 1063
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Because of the polynomial factorization, the Stella Octangula numbers can never be prime. They are semiprime when n = is prime and 2*n^2-1 is also prime. That is, the n-th Stella Octangula number is semiprime for n = 2, 3, 7, 11, 13, 17, 41, 43, 59, 73, 109, 113, 127, 137, 157, 179, 181, 197, 199, ....
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LINKS
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J. V. Post, Table of Polytope Numbers, Sorted, Through 1,000,000
Eric Weisstein's World of Mathematics, Stella Octangula Number
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FORMULA
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a(n) is in this sequence iff A007588(a(n))) is an element of A001358. a(n) is in this sequence iff A106482(a(n)) = 2. a(n) is in this sequence iff a(n) is prime and 2*a(n)^2-1 is also prime.
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EXAMPLE
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73 is in this sequence because the 73rd Stella Octangula number = 73*(2*73^2 - 1) = 777961 = 73 * 10657, which is semiprime.
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MATHEMATICA
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Select[Table[Prime[n], {n, 500}], PrimeQ[2*#^2 - 1] &] (*Chandler*)
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CROSSREFS
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Cf. A000040, A001358, A007588, A106482, A106484.
Sequence in context: A045322 A023221 A127430 this_sequence A040116 A014580 A091206
Adjacent sequences: A106480 A106481 A106482 this_sequence A106484 A106485 A106486
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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), May 03 2005
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), May 03 2005
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