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Record values in A228098.
2

%I #38 Jan 29 2023 15:06:22

%S 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,

%T 36,39

%N Record values in A228098.

%C The corresponding index values are ranks of prime numbers and are in A230777; corresponding primes are in A230778.

%C 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).

%C 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.

%t 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 *)

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

%K nonn,more

%O 1,2

%A _Jean-Christophe Hervé_, Nov 01 2013

%E a(13)-a(28) from _Martin Ehrenstein_, Jun 06 2021