Sums of the Fibonacci and Lucas numbers over the binary digital sums

Authors : Teerapat SRİCHAN

Pages : 286-289

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Publication Date : 2018-10-15

Article Type : Research Paper

Abstract :Let $sinsert ignore into journalissuearticles values(n);$ denote the binary digital sum of the positive integer $n$. Using elementary combinatorial method, we present some known identities as a new form in term of $sinsert ignore into journalissuearticles values(n);$. The sums of the Fibonacci, Lucas and harmonic numbers over the binary digital sums are considered. Moreover, we also give the sums over the binary digital sums, which derived from the binomial theorem.
Keywords : binary digital sum, Fibonacci number, harmonic number, Lucas number