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

%I #14 May 18 2024 14:58:00

%S 1,1,1,3,4,4,14,13,16,48,55,50,173,148,147,665,580,559,1920,1447,1975,

%T 6240,4228,5689,15764,17562,14332,46207,39071,35317,172311,134752,

%U 110758,381384,299971,479935,1154568,733900,1027967,2581763,2636545,2333308

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

%C Of the patterns counted by A023192, the number of those that start and end with a prime. - _Sean A. Irvine_, May 27 2019

%e From _Jon E. Schoenfield_, May 17 2024: (Start)

%e 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.

%e .

%e n 2n-1 a(n) prime patterns

%e - ---- ---- --------------------------------------------------

%e 1 1 1 p

%e 2 3 1 pcp

%e 3 5 1 pcccp

%e 4 7 3 pcccccp, pcpcccp, pcccpcp

%e 5 9 4 pcccccccp, pcpcccccp, pcccccpcp, pcpcccpcp

%e 6 11 4 pcccccccccp, pcccpcccccp, pcccccpcccp, pcccpcpcccp

%e 7 13 14 pcccccccccccp, pcpcccccccccp, pcccpcccccccp,

%e pcccccpcccccp, pcccccccpcccp, pcccccccccpcp,

%e pcpcccpcccccp, pcpcccccpcccp, pcccpcpcccccp,

%e pcccpcccccpcp, pcccccpcpcccp, pcccccpcccpcp,

%e pcpcccpcpcccp, pcccpcpcccpcp

%e (End)

%Y Cf. A023190, A023191, A023192.

%K nonn,more

%O 1,4

%A _David W. Wilson_

%E Name edited by _Jon E. Schoenfield_, May 17 2024