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<p>We study a problem of Douglass and Ono concerning the smallest integer <i>n</i> such that the partition function <i>p</i>(<i>n</i>) begins with a specified string of digits <i>f</i> in base <i>b</i>. By employing an elementary discrepancy framework, we establish new upper bounds that significantly improve upon previous results of Luca.</p>

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On the Digits of Partition Functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月5日

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  • Siddharth Iyer

摘要

We study a problem of Douglass and Ono concerning the smallest integer n such that the partition function p(n) begins with a specified string of digits f in base b. By employing an elementary discrepancy framework, we establish new upper bounds that significantly improve upon previous results of Luca.