OEIS A000038: The 2,0,0,0… Sequence and Its Web of Connections

We dive into A000038, a deceptively simple OEIS entry that starts with 2 and then zeros. We'll explain how it's described as twice A00007 and how that relation lets us see A000038 as a shifted, doubled building block— a doorway into a larger network of sequences. We discuss the formula involving A00000 and the prime counting function, plus the Mathematica and Prague sections that show how to generate terms with code. We'll touch on the cross-references to Euler's totient function and the ways this tiny sequence intersects group theory and even machine learning, illustrating the power of the OEIS as a collaborative, interconnected library.

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