LINKS
Chai Wah Wu, <a href="/A232894/b232894_1.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..200 from Zhi-Wei Sun)
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Chai Wah Wu, <a href="/A232894/b232894_1.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..200 from Zhi-Wei Sun)
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Zhi-Wei Sun, Chai Wah Wu, <a href="/A232894/b232894_1.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..200</a> from Zhi-Wei Sun)
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(ii) For any integer n > 3, neither Catalan(n) - n nor Catalan(n) + n has the form x^m with m, > 1 and x > 1.
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Least positive integer m <= n^2/2 + 7 such that {Catalan(k) - k: k = 1, ..., m} contains a complete system of residues modulo n, or 0 if such a number m does not exist.
Conjecture: (i) Let n be any positive integer. Then we have 0 < a(n) > 0<= n^2/2 + 7. Also, {Catalan(k) + k: k = 1, ..., [n^2/2] + 23} contains a complete system of residues modulo n, where [.] is the floor function.
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