Journal of the Ramanujan Mathematical Society

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Sequences of Positive Integers Containing no p Terms in Arithmetic Progression Generated by the Greedy Algorithm


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1 Dept. of Mathematics, RCC-Institute of Information Technology, South Canal Road, Beliaghata, Kolkata-700015, India
     

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Let Sp be the set of positive integers containing no p terms in arithmetic progression generated by the greedy algorithm. We show that for p an odd prime, the set Sp does not maximize the sum ∑a∈A 1/a , where the set A runs over all sequences of positive integers containing no p terms in arithmetic progression.
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  • Sequences of Positive Integers Containing no p Terms in Arithmetic Progression Generated by the Greedy Algorithm

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Authors

Goutam Pal
Dept. of Mathematics, RCC-Institute of Information Technology, South Canal Road, Beliaghata, Kolkata-700015, India

Abstract


Let Sp be the set of positive integers containing no p terms in arithmetic progression generated by the greedy algorithm. We show that for p an odd prime, the set Sp does not maximize the sum ∑a∈A 1/a , where the set A runs over all sequences of positive integers containing no p terms in arithmetic progression.