OFFSET
1,5
FORMULA
Conjecture: Limit_{n->oo} log(a(n))/(n*log(n)) = c ~ 0.13... .
EXAMPLE
MATHEMATICA
a[n_] := Count[Prime[n] * Divisors[Product[Prime[i], {i, 1, n - 1}]], _?(PrimeQ[# - 1] && PrimeQ[# + 1] &)]; Array[a, 10]
PROG
(Python)
from math import prod
from itertools import combinations
from sympy import primerange, prime, isprime
def A354950(n):
plist = list(primerange(2, p:=prime(n)))
return sum(1 for l in range(1, n) for d in combinations(plist, l) if isprime((q:= prod(d)*p)-1) and isprime(q+1)) # Chai Wah Wu, Jun 14 2022
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Jun 13 2022
STATUS
approved