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Search: id:A100481
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| A100481 |
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Greatest prime factor in A095117(n) = greatest prime factor in n + pi(n) where pi(n) is the prime counting function = greatest prime factor in n + A000720(n). |
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+0
1
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| 1, 3, 5, 3, 2, 3, 11, 3, 13, 7, 2, 17, 19, 5, 7, 11, 3, 5, 3, 7, 29, 5, 2, 11, 17, 7, 3, 37, 13, 5, 7, 43, 11, 5, 23, 47, 7, 5, 17, 13, 3, 11, 19, 29, 59, 5, 31, 7, 2, 13, 11, 67, 23, 7, 71, 3, 73, 37, 19, 11, 79, 5, 3, 41, 83, 7, 43, 29, 11, 89, 13, 23, 47, 19, 3, 97, 7, 11, 101, 17, 103
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Conjecture: every prime appears infinitely often in this sequence.
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REFERENCES
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Guy, R. K. "The Largest Prime Factor of n." B46 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 101, 1994.
Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, 1993.
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LINKS
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Andrew Booker, The Nth Prime Page.
Eric Weisstein's World of Mathematics, "Prime Counting Function."
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FORMULA
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a(n) = A006530(n + A000720(n)) = greatest prime factor in (n + A000720(n)).
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EXAMPLE
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a(1) = 1 = A006530(1+0).
a(3) = 5 because 3 + pi(3) = p + number of primes equal or less than 3, of which there are 2 (namely 2 and 3) hence a(3) = 3 + 2 = 5. This is prime, hence equal to its greatest prime factor. a(5) = 2 because 5 + pi(5) = 5 + 3 = 2 * 2 * 2 hence the greatest prime factor is 2.
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CROSSREFS
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Cf. A000720, A006530, A095117.
Sequence in context: A021743 A057023 A085849 this_sequence A101778 A161670 A135514
Adjacent sequences: A100478 A100479 A100480 this_sequence A100482 A100483 A100484
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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), Nov 22 2004
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 27 2004
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