OFFSET
1,2
COMMENTS
The corresponding index values are ranks of prime numbers and are in A230777; corresponding primes are in A230778.
A228098(n) is the number of primes p > prime(n) and such that p*prime(n) < prime(n+1)^2. This value is related to the distribution of primes around prime(n+1). High values correspond to a large gap before prime(n+1) followed by several small gaps after prime(n+1).
There is no value > 14 in the first 100000 terms of A228098, and only one equal to 14: A228098(31545), which corresponds to prime(31545) = 370261. However, 12 appears 2 times after 14: A228098(59257) = A228098(88280) = 12 (prime(59257) = 736279 and prime(88280) = 1138273); and 13 one time for prime(66762) = 838249.
MATHEMATICA
DeleteDuplicates[Table[PrimePi[Prime[n+1]^2/Prime[n]]-n, {n, 100000}], GreaterEqual] (* The program generates the first 12 terms of the sequence. *) (* Harvey P. Dale, Jan 29 2023 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jean-Christophe Hervé, Nov 01 2013
EXTENSIONS
a(13)-a(28) from Martin Ehrenstein, Jun 06 2021
STATUS
approved