A023191 -id:A023191 - cp's OEIS frontend

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

David W. Wilson

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

			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)

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

Cf. A023190, A023191, A023192.

Name edited by Jon E. Schoenfield, May 17 2024

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

A023190 Conjecturally, maximum number of primes in an infinitely-recurring prime pattern of width 2*n-1.

Original entry on oeis.org

1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 6, 7, 8, 8, 9, 10, 10, 11, 10, 11, 12, 12, 12, 13, 14, 13, 14, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 20, 20, 21, 21, 21, 22, 22, 23, 23, 23, 24, 24, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30

Offset: 1

David W. Wilson

nonn

Of all the patterns in A023192 (i.e. infinitely-recurring prime patterns) for length 2*n-1, consider those starting and ending with "p". This sequence gives the maximal count of "p"'s in any of those patterns. The companion sequence A023191, gives the number of patterns achieving that maximum. - Sean A. Irvine, May 27 2019

			a(3) concerns patterns of length 5. Of the 10 potential patterns (ccccc, ccccp, cccpc, ccpcc, cpccc, pcccc, ccpcp, cpcpc, pcpcc, pcccp), only pcccp starts and ends with a "p", and it contains 2 "p"'s, so a(3) = 2, and A023191(3) = 1. - _Sean A. Irvine_, May 27 2019

Martin Raab, Table of n, a(n) for n = 1..1166
Thomas J Engelsma, Permissible Patterns

Cf. A023191, A023192.

More terms from Thomas J Engelsma web page added by Martin Raab, Oct 31 2021

cp's OEIS Frontend

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

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