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A117739
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Decimal expansion of the largest C_0 = 1.2209864... such that for C < C_0 and A < 2 the sequence a(n) = floor[A^(C^n)] can't contain only prime terms.
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4
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1, 2, 2, 0, 9, 8, 6, 4, 0, 7, 1, 3, 9, 5, 5, 0, 2, 4, 4, 2, 7, 3, 7, 0, 1, 4, 5, 1, 8, 8, 3, 5, 5, 8, 1, 4, 1, 6, 4, 6, 2, 4, 7, 5, 4, 0, 6, 0, 2, 9, 3, 8, 4, 4, 4, 7, 9, 1, 9, 7, 2, 9, 2, 5, 3, 7, 5, 1, 0, 3, 8, 7, 9, 7, 4, 6, 0, 0, 9, 1, 9, 1, 0, 3, 4, 2
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OFFSET
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1,2
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COMMENTS
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It is not proved that for C > C_0 the mentioned infinite sequence of primes actually exists. However, heuristics show that A243358 could be infinite (the decimal expansion of corresponding A value is A243370).
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LINKS
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FORMULA
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C_0 can be estimated as (logP/log84)^(1/k), where P is k+10th term of A243358.
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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