A sequence prediction puzzle

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All About Countable Saturation (Ultra Series 7)
Ultraproducts and Compactness (Ultra Series 6)
Infinitely Large Primes (Ultra Series 5)
Ultraproducts and Łoś’s Theorem (Ultra Series 4)
Hypernaturals in all their glory (Ultra Series 3)
Hypernaturals Simplified (Ultra Series 2)
Ultrafilters, Ultraproducts, and Hypernaturals 1: Introduction
Even Numbers are Tautologies
Notes on motivation and self-improvement
First Order Truth Trees
One nonstandard is worth infinitely many standards
This post is lying to you
Some half-baked thoughts on moral arbitrariness
Asymmetry between the infinite and finite
PA doesn’t trust its provability predicate
No more than half of anti-sets are big
A Dating Puzzle, and Bayesian Experimental Design
What precedent does the Trump Twitter ban set?
Divisibility Tricks and Orderly Numbers
What’s the probability that an election winner leads throughout the entire vote?
Quantum Chess
Biblical inerrancy
Formal Semantics 1: Historical Prelude and Compositionality
Two more short and sweet proofs of propositional compactness
The Theory of Knots