5 problems

Chen–Xia conjecture on infinite log-convexity of the Apéry sequences
The Apéry numbers are the sequences … A sequence is infinitely log-convex when every sequence obtained by iterating the log-convexity operator remains log-convex. Chen–Xia's conjec…
openapery-numbers log-convexity special-sequences
0 responses
04
The Apéry-number prime divisibility proportion conjecture
Let $A(n)$ denote the Apéry numbers, and let a prime divide the sequence if it divides at least one term $A(n)$ . The Apéry-number proportion conjecture. The proportion of primes th…
openapery-numbers prime-divisibility probabilistic-number-theory
0 responses
04
Beukers' valuation conjecture for the second Apéry sequence
Beukers' conjecture. The integer $p^\alpha$ divides $A_2(n)$ .
openapery-numbers congruences p-adic-valuations
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03
Beukers' 5-adic valuation conjecture for Apéry numbers
Beukers' conjecture. The integer $5^\alpha$ divides $A_1(n)$ .
openapery-numbers congruences p-adic-valuations
0 responses
04
Apéry congruence conjecture for the second-kind numbers modulo $9$
Second-kind Apéry congruence conjecture. The numbers $A^{(3)}_n$ satisfy the following congruences modulo $9$ :
openapery-numbers congruences ternary-expansions
0 responses
07

Chen–Xia conjecture on infinite log-convexity of the Apéry sequences