OEIS A000155: Rounding the Modified Bessel Function K_1 to Integers

An accessible tour of A000155—the nearest integer to the modified Bessel function K_1(n). We unpack what “modified Bessel” means, why rounding a continuous function yields a discrete sequence (with early terms 0, 1, 2, 7, 4, 4, 3, 6, 1, …), and what this reveals about the bridge between continuous analysis and integer sequences. We’ll show how to generate terms with Maple or Mathematica, point to Abramowitz and Stegun, and explore the OEIS’s cross-references to related sequences and parameter variations (e.g., changing the input to the Bessel function) to map a family of connected sequences.

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