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Search: id:A094106
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| A094106 |
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a(n) = maximal length L of a "power floor prime" sequence, i.e. a sequence of the form [x^k], k=1,2,..,L consisting of primes only, where [x] is the n-th prime number. |
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+0
1
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| 8, 7, 8, 5, 10, 12, 16, 14, 18, 22, 24, 26, 27, 28, 34, 35, 37, 39, 40, 45, 43, 46, 49, 51, 55, 57
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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Crandall and Pomerance, "Prime numbers, a computational perspective", p. 69, Research Problem 1.75.
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LINKS
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C. Rivera, Problem 42
C. Rivera, Puzzle 227
Eric Weisstein's World of Mathematics, Power Floor Prime Sequence
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EXAMPLE
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a(1)=8 because for x=111/47 the sequence [x^k],k=1,2,... 2,5,13,31,73,173,409,967,.. starts with 8 primes and this is the maximum for any x with [x]=2. (Compare also A063636, though the rational number x= 1287/545 used there is not of minimal height!)
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CROSSREFS
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Cf. A076255, A076357.
Sequence in context: A086911 A103984 A037077 this_sequence A021536 A094082 A019326
Adjacent sequences: A094103 A094104 A094105 this_sequence A094107 A094108 A094109
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KEYWORD
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nonn
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AUTHOR
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Johann Wiesenbauer (j.wiesenbauer(AT)tuwien.ac.at), May 02 2004. a(22) = 46 sent Jun 03 2004.
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EXTENSIONS
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a(23) = 49 from Johann Wiesenbauer (j.wiesenbauer(AT)tuwien.ac.at), Jun 27 2004
a(24) = 51 from Johann Wiesenbauer (j.wiesenbauer(AT)tuwien.ac.at), Aug 08 2004
a(25) and a(26) Michael Kenn (michael.kenn(AT)philips.com), Jan 03 2006, who says: To achieve this results I used a shared network of 37 computers over the Christmas holidays. The total calculation time was equivalent to slightly more than 1 CPU year of a P4 - 2,4GHz.
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