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A066352
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Pillai sequence: a(n) is the smallest term in A007924 requiring n primes.
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7
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OFFSET
| 0,3
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COMMENTS
| a(5) computed independently in 2007 by Richard Mathar and Luca & Thangadurai, both using Thomas Nicely's tables.
On Cramer's conjecture, the number of primes required is O(log* n), where log* is the iterated logarithm, so the rate of growth of a(n) is tetrational in n. [Charles R Greathouse IV, Aug 28 2010]
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REFERENCES
| S. S. Pillai, "An arithmetical function concerning primes", Annamalai University Journal (1930), pp. 159-167.
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LINKS
| Florian Luca, Ravindranathan Thangadurai, On an arithmetic function considered by Pillai, Journal de theorie des nombres de Bordeaux 21:3 (2009), pp. 695-701.
M. T. Marcos, Smarandache Prime Base representation, prime puzzle 141.
Thomas R. Nicely, First occurrence prime gaps
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FORMULA
| a(n) = 2*p(m) - p(m-1) with minimal m = pi(a(n)) so that p(m) = a(n-1) + p(m-1), where p(n) is A008578(n).
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EXAMPLE
| The greatest prime <= 27 is 23; the greatest prime <= 27-23 is 3; 27-23-3 = 1, so the Pillai representation of 27 is 23+3+1, which uses more terms than all preceding numbers.
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CROSSREFS
| Cf. A007924.
Sequence in context: A066842 A133032 A110763 * A051674 A132641 A008973
Adjacent sequences: A066349 A066350 A066351 * A066353 A066354 A066355
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KEYWORD
| nonn,hard
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AUTHOR
| Copied from www.primepuzzles.net by Frank Ellermann (hmdmhdfmhdjmzdtjmzdtzktdkztdjz(AT)gmail.com), Dec 19 2001.
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EXTENSIONS
| Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 28 2009
Entry rewritten by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Aug 28 2010
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