Abstract
Let \(g \geqslant 2\) be an integer and \(S_g(n)\) denote the sum of the digits in base g of the positive integer n. We obtain asymptotic formulas for the number of odd integers up to x that can be written as a product pq, with p, q both primes, satisfy \(S_g(p) \equiv S_g(q) \equiv a ~\mathrm{mod}\,~ b\ (b \geqslant 2, a \in {\mathbb {Z}})\). So, we observe a large bias amongst such integers.
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Acknowledgements
The author would like to thank Professor Mondher Ben Jemaa for many helpful conversations on this problem. The author also thanks the referee for careful reading and valuable suggestions.
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Communicated by Rosihan M. Ali.
In memory of Professor Christian Mauduit.
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Wannes, W. Large Bias Amongst Products of Two Primes. Bull. Malays. Math. Sci. Soc. 45, 623–629 (2022). https://doi.org/10.1007/s40840-021-01209-5
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DOI: https://doi.org/10.1007/s40840-021-01209-5