EPISODE · Jul 19, 2025 · 5 MIN
OEIS A000280: Exploding growth from a simple cubic recurrence
from Intellectually Curious · host Mike Breault
We explore A000280, defined by a_n = a_{n-1} + (a_{n-2})^3 with a_0 = 0, a_1 = 1. The early terms 0, 1, 1, 2, 3, 11, 38 hint at rapid escalation; by A12 the term has 85 digits, illustrating explosive growth uncommon for simple recurrences. The dominant asymptotic is A_n ~ C^{3^n/2}, with a constant C that varies slightly with parity. We unpack why the cubic term triggers super-exponential growth, the nested exponent structure it implies, and what that means for computation and number theory. We'll note metadata points: A000280 is a nonnegative-integers sequence and has cross-links to related sequences such as A000278. Finally, we invite listeners to reflect on how tiny rules can lead to enormous complexity and to explore more OEIS entries for similar phenomena.Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information.Sponsored by Embersilk LLC
What this episode covers
We explore A000280, defined by a_n = a_{n-1} + (a_{n-2})^3 with a_0 = 0, a_1 = 1. The early terms 0, 1, 1, 2, 3, 11, 38 hint at rapid escalation; by A12 the term has 85 digits, illustrating explosive growth uncommon for simple recurrences. The dominant asymptotic is A_n ~ C^{3^n/2}, with a constant C that varies slightly with parity. We unpack why the cubic term triggers super-exponential growth, the nested exponent structure it implies, and what that means for computation and number theory. ...
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OEIS A000280: Exploding growth from a simple cubic recurrence
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