The Raise-the-Bar sequence.

A sequence of Shannon. Written by Michael Thomas De Vlieger, St. Louis, Missouri, 2023 0111.

Abstract.

Scott Shannon wrote a sequence that requires all prime divisors of the sum of 2 adjacent terms to divide the following term. This leads to a sequence that exhibits phases wherein all terms are divisible by a “sticky” prime, raising the bar for numbers that endeavor to enter the sequence. The phases show in scatterplot as a series of escalating scallops. The sticky primes conglomerate into a sticky composite factor that continues to grow as n increases. This sticky factor yields interesting implications for subsequent terms in the sequence.

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Concerns OEIS sequences:

A002110, A007947, A339557.

To cite:

Michael Thomas De Vlieger, The Raise-the-Bar Sequence, Simple Sequence Analysis, Article 20230111.