OEIS A000301: Fibonacci Exponentiated Sequence
from Intellectually Curious Hosted by Mike Breault
We explore the Fibonacci-exponentiated sequence A000301, which has two elegant definitions: a_n = a_{n-1} a_{n-2} with a_0 = 1, a_1 = 2, and a_n = 2^{F_n}, where F_n is the nth Fibonacci number. We discuss how these two views produce the same sequence, and what that harmony reveals about connections to Fibonacci growth, the golden ratio, and its appearance in continued fractions of related constants (A073115) and the rabbit constant. This episode highlights how a simple pattern can echo across discrete and continuous realms. Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information. Sponsored by Embersilk LLC
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We explore the Fibonacci-exponentiated sequence A000301, which has two elegant definitions: a_n = a_{n-1} a_{n-2} with a_0 = 1, a_1 = 2, and a_n = 2^{F_n}, where F_n is the nth Fibonacci number. We discuss how these two views produce the same sequence, and what that harmony reveals about connections to Fibonacci growth, the golden ratio, and its appearance in continued fractions of related constants (A073115) and the rabbit constant. This episode highlights how a simple pattern can echo acros...
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