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A123341
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a(1) = 1, a(n) = Sum_{k=1}^{Pi(n)} a(n-k) for n > 1, where Pi(n) is the number of primes less than or equal to n.
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0
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1, 1, 2, 3, 6, 11, 22, 42, 81, 156, 312, 613, 1226, 2430, 4818, 9555, 19110, 38064, 76128, 151944, 303275, 605324, 1210648, 2418866, 4832914, 9656273, 19293436, 38548808, 77097616, 154119104, 308238208, 616324472, 1232345669, 2464086014
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OFFSET
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1,3
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COMMENTS
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Conjecture: lim_{n->infinity} a(n)/2^n > 0; appears to be about 0.1432645404.
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LINKS
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FORMULA
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a(1) = a(2) = 1, for p an odd prime, a(p) = 2a(p-1), otherwise a(n) = 2a(n-1) - a(n - pi(n) - 1).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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