A023189 - OEIS

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

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OFFSET

1,4

COMMENTS

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

LINKS

Table of n, a(n) for n=1..42.

EXAMPLE

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,