A230776 Record values in A228098.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 18, 20, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 36, 39

Offset: 1

Author

Jean-Christophe Hervé, Nov 01 2013

Keywords

• nonn
• more

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.

Crossrefs

Cf. A000040, A001223, A228098, A230777, A230778.

Programs

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 *)

Extensions

a(13)-a(28) from Martin Ehrenstein, Jun 06 2021