4 problems

Let $r(n)$ denote the digit reversal of $n$ in base ten, and let $v(n)$ be the sum of the primes and exponents appearing in the prime factorization of $n$. Uniqueness conjecture fo…

Let $v(n)$ denote the sum of the primes and exponents appearing in the prime factorization of $n$, and let $r_{10}(n)$ be the digit reversal of $n$ in base ten. A $v$-palindrome in…

Let $v(n)$ denote the sum of the primes and exponents appearing in the prime factorization of $n$, and let $r_b(n)$ be the digit reversal of $n$ in base $b$. A $v$-palindrome in ba…

Let $b_0=0$, $b_1=1$, and, with $\tau=\sqrt{2}$, define … for $n\geq 0$. Here $\log_3$ denotes the logarithm to base $3$. Northshield's conjecture. … Northshield proved the corresp…