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May 7, 2026Annals of Combinatorics0 citationsOpen Access

On the Digits of Partition Functions

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SISiddharth Iyer

Key Points

  • This research examines integer values associated with the partition function and their initial digits in specific bases.
  • Utilized an elementary discrepancy framework
  • Analyzed the relationship between integers and partition function digits
  • Established new upper bounds on the integer n
  • Found significant improvements over previous results reported by Luca
  • Specified conditions for the initial digits of the partition function p
  • Defined upper bounds that clarify the structure of partition functions

Abstract

Abstract 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.

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Cite This Study

Siddharth Iyer (2026) studied this question.

synapsesocial.com/papers/69fbe2b3164b5133a91a2143https://doi.org/10.1007/s00026-026-00827-9
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