A230777 Indices of record values in A228098.

1, 2, 4, 30, 180, 462, 890, 1532, 3385, 19871, 29040, 31545, 597311, 1293698, 2279181, 118374763, 821495413, 2247521689, 3145845927, 7650216016, 22859974504, 78076882908, 189573830057, 223393027147, 435001965071, 637259184969, 821040118481, 1562199136511

Offset: 1

Author

Jean-Christophe Hervé, Nov 01 2013

Keywords

• nonn

Comments

These indices are ranks of prime numbers; corresponding primes are in A230778, and corresponding record values are in A230776.

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.

Crossrefs

Cf. A000040, A001223, A228098, A230776, A230778.

Extensions

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