cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A230777 Indices of record values in A228098.

Original entry on oeis.org

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

Views

Author

Jean-Christophe Hervé, Nov 01 2013

Keywords

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

A230776 Record values in A228098.

Original entry on oeis.org

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

Views

Author

Jean-Christophe Hervé, Nov 01 2013

Keywords

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
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.