Lucas numbers that are palindromic concatenations of two distinct repdigits

Let $\{L_n\}_{n\geq 0}$ be the sequence of Lucas numbers. In this paper, we determine all Lucas numbers that are palindromic concatenations of two distinct repdigits.Comment: 12 page

On the Largest Prime factor of the k-generalized Lucas numbers

Let $(L_n^{(k)})_{n\geq 2-k}$ be the sequence of $k$--generalized Lucas numbers for some fixed integer $k\ge 2$ whose first $k$ terms are $0,\ldots,0,2,1$ and each term afterwards is the sum of the preceding $k$ terms. For an integer $m$, let $P(m)$ denote the largest prime factor of $m$, with $P(0)=P(\pm 1)=1$. We show that if $n \ge k + 1$, then $P (L_n^{(k)} ) > (1/86) \log \log n$. Furthermore, we determine all the $k$--generalized Lucas numbers $L_n^{(k)}$ whose largest prime factor is at most $7$

On the multiplicity in Pillai\u27s problem with Fibonacci numbers and powers of a fixed prime

Let ( {F_n}_{ngeq 0} ) be the sequence of Fibonacci numbers and let (p) be a prime. For an integer (c) we write (m_{F,p}(c)) for the number of distinct representations of (c) as (F_k-p^ell) with (kge 2) and (ellge 0). We prove that (m_{F,p}(c)le 4)

General anaesthetic and airway management practice for obstetric surgery in England: a prospective, multi-centre observational study

There are no current descriptions of general anaesthesia characteristics for obstetric surgery, despite recent changes to patient baseline characteristics and airway management guidelines. This analysis of data from the direct reporting of awareness in maternity patients' (DREAMY) study of accidental awareness during obstetric anaesthesia aimed to describe practice for obstetric general anaesthesia in England and compare with earlier surveys and best-practice recommendations. Consenting patients who received general anaesthesia for obstetric surgery in 72 hospitals from May 2017 to August 2018 were included. Baseline characteristics, airway management, anaesthetic techniques and major complications were collected. Descriptive analysis, binary logistic regression modelling and comparisons with earlier data were conducted. Data were collected from 3117 procedures, including 2554 (81.9%) caesarean deliveries. Thiopental was the induction drug in 1649 (52.9%) patients, compared with propofol in 1419 (45.5%). Suxamethonium was the neuromuscular blocking drug for tracheal intubation in 2631 (86.1%), compared with rocuronium in 367 (11.8%). Difficult tracheal intubation was reported in 1 in 19 (95%CI 1 in 16-22) and failed intubation in 1 in 312 (95%CI 1 in 169-667). Obese patients were over-represented compared with national baselines and associated with difficult, but not failed intubation. There was more evidence of change in practice for induction drugs (increased use of propofol) than neuromuscular blocking drugs (suxamethonium remains the most popular). There was evidence of improvement in practice, with increased monitoring and reversal of neuromuscular blockade (although this remains suboptimal). Despite a high risk of difficult intubation in this population, videolaryngoscopy was rarely used (1.9%)