On the binary expansion of the odd Catalan numbers
نویسندگان
چکیده
Let cn = 1 n + 1 ( 2n n ) be the nth Catalan number. In this paper, we look at some of the arithmetic properties of cn. For example, we show that w2(cn) ! log log n for all n ! 3 provided that cn is odd, where w2(m) is the Hamming weight (or the binary sum of digits) of the positive integer m. We also determine all instances in which cn is a base 2 palindrome, and prove that the first k odd Catalan numbers are always distinct modulo 2k+1.
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