A023189 Conjecturally, number of infinitely recurring prime patterns of width 2n-1.

1, 1, 1, 3, 4, 4, 14, 13, 16, 48, 55, 50, 173, 148, 147, 665, 580, 559, 1920, 1447, 1975, 6240, 4228, 5689, 15764, 17562, 14332, 46207, 39071, 35317, 172311, 134752, 110758, 381384, 299971, 479935, 1154568, 733900, 1027967, 2581763, 2636545, 2333308, 8369027, 5516720, 6043194

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• changed

Comments

Of the patterns counted by A023192, the number of those that start and end with a prime. - Sean A. Irvine, May 27 2019

Examples

			From _Jon E. Schoenfield_, May 17 2024: (Start)
The table below lists every (conjecturally) infinitely recurring prime pattern of width 2n-1 for n = 1..7. Each p represents a prime; each c represents a composite.
.
  n  2n-1  a(n)  prime patterns
  -  ----  ----  --------------------------------------------------
  1     1     1  p
  2     3     1  pcp
  3     5     1  pcccp
  4     7     3  pcccccp, pcpcccp, pcccpcp
  5     9     4  pcccccccp, pcpcccccp, pcccccpcp, pcpcccpcp
  6    11     4  pcccccccccp, pcccpcccccp, pcccccpcccp, pcccpcpcccp
  7    13    14  pcccccccccccp, pcpcccccccccp, pcccpcccccccp,
                 pcccccpcccccp, pcccccccpcccp, pcccccccccpcp,
                 pcpcccpcccccp, pcpcccccpcccp, pcccpcpcccccp,
                 pcccpcccccpcp, pcccccpcpcccp, pcccccpcccpcp,
                 pcpcccpcpcccp, pcccpcpcccpcp
(End)
		

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..60

Crossrefs

Cf. A023190, A023191, A023192.

Extensions

Name edited by Jon E. Schoenfield, May 17 2024

a(43)-a(45) from Pontus von Brömssen, Aug 25 2025