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Search: id:A104238
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| A104238 |
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Positive integers n such that n^5 + 1 is semiprime. |
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+0
14
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| 2, 10, 12, 16, 22, 126, 136, 180, 256, 268, 276, 366, 388, 396, 438, 462, 606, 642, 652, 658, 676, 738, 760, 768, 982, 1012
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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n^5+1 can only be prime when n = 1, n^5+1 = 2. This is because of the polynomial factorization n^5+1 = (n+1) * (n^4 - n^3 + n^2 - n + 1). Hence after the initial n=1 prime, the binomial can at best be semiprime and that only when both (n+1) and (n^4 - n^3 + n^2 - n + 1) are primes.
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FORMULA
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a(n)^5 + 1 is semiprime. a(n)+1 is prime and a(n)^4 - a(n)^3 + a(n)^2 - a(n) + 1 is prime.
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EXAMPLE
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n n^5+1 = (n+1) * (n^4 - n^3 + n^2 - n + 1)
2 33 = 3 * 11
10 100001 = 11 * 9091
12 248833 = 13 * 19141
16 1048577 = 17 * 61681
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CROSSREFS
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Cf. A000040, A001538, A103854.
Adjacent sequences: A104235 A104236 A104237 this_sequence A104239 A104240 A104241
Sequence in context: A053449 A060248 A092385 this_sequence A053069 A130842 A061818
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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).com), Apr 02 2005
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