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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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9
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OFFSET
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0,3
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COMMENTS
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a(5) computed independently in 2007 by R. J. 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
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S. S. Pillai, "An arithmetical function concerning primes", Annamalai University Journal (1930), pp. 159-167.
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LINKS
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FORMULA
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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
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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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PROG
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print1(r=0); for(n=1, 1e7, if(A072491(n)>r, r=a(n); print1(", "n)))
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CROSSREFS
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KEYWORD
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nonn,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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