Teensy Problems: Sum of Factorials
Let $\mathrm{sf}(n)$ be the sum-of-factorials function: $0! + 1! + … n!$. Its first few values are $1$, $2$, $4$, $10$, $34$, ….
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teensy-problems
Teensy Problems: Falling Leaves
Autumn and Yvonne love to play “falling leaves” this time of year. They play on a tree containing some number of leaves (possibly none) on its left and right...
Teensy Problems: Coprime Labeling
Let $G$ be a graph with $n$ vertices. We say a graph is coprimely labeled if its vertices are labeled using all the integers from 1 to $n$ in such a way wher...
Teensy Problems: Marvin Numbers
Marvin is interested in numbers whose sum of their digits equals the product of their digits. Call a nonnegative integer a $b$-Marvin number if it has this p...
Teensy Problems: Counting Carol
Carol really likes counting, but can only keep track of so many numbers at once. She’s devised a family of sequences that matches these aptitudes, in the fol...
Teensy Problems: Finn Factor
Finn Factor just learned about a neat way to compute the prime numbers. Let $S$ be the list of known primes (initially empty), and start at $n = 2$. For each...