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Search: id:A097822
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| A097822 |
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Numbers n such that n^2+n+41 (Euler's "prime generating polynomial") has more than 2 prime factors. |
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2
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| 420, 431, 491, 492, 514, 533, 573, 574, 603, 614, 655, 686, 738, 775, 798, 858, 861, 890, 995, 901, 904, 917, 919, 942, 984, 989, 1025, 1059, 1116, 1130, 1162, 1169, 1188, 1215, 1222, 1224, 1245, 1251, 1253, 1268, 1271, 1318, 1321, 1334, 1365, 1374, 1407
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OFFSET
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1,1
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COMMENT
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All visible sequence terms give exactly 3 prime factors. The smallest composite of the form p(n)=n^2+n+41 with 4 prime factors occurs for p(1721)=2963603=43*41^3. Smallest n with 4 distinct prime factors: p(2911)=8476873=83*53*47*41, smallest n with 5 prime factors: p(14144)=200066921=47^4*41, smallest n with 5 distinct prime factors: p(38913)=1514260523=173*71*61*47*43.
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LINKS
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Eric Weisstein's World of Mathematics, Prime-Generating Polynomial
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EXAMPLE
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a(1)=420 because 420^2+420+41=176861=71*53*47 is the first n for which p(n)=n^2+n+41 has more than 2 prime factors. For all smaller n p(n) is either prime or semiprime.
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CROSSREFS
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Cf. A002837 n such that n^2-n+41 is prime, A007634 n such that n^2+n+41 is composite ("is semiprime" would also fit because all visible sequence terms produce semiprimes), A005846 primes of form n^2+n+41, A097823 n^2+n+41 is not square-free.
Sequence in context: A060230 A130737 A061118 this_sequence A069064 A024410 A070237
Adjacent sequences: A097819 A097820 A097821 this_sequence A097823 A097824 A097825
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Aug 26 2004
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