A023192 Conjecturally, number of infinitely-recurring prime patterns on n consecutive integers.

2, 3, 5, 7, 10, 13, 19, 25, 35, 45, 59, 73, 101, 129, 170, 211, 268, 325, 430, 535, 695, 855, 1065, 1275, 1658, 2041, 2572, 3103, 3781, 4459, 5802, 7145, 9068, 10991, 13473, 15955, 20357, 24759, 30608, 36457, 44281, 52105, 66169, 80233, 98525, 116817, 140798, 164779

Offset

1,1

Links

Pontus von Brömssen, Table of n, a(n) for n = 1..120 (terms 1..76 from Sean A. Irvine)

Sean A. Irvine, Java program (github)

Formula

a(n) = 1 + Sum_{k=1..floor((n+1)/2)} (n-2*k+2)*A023189(k). - Pontus von Brömssen, Aug 25 2025

Example

a(3) = 5: Conjecturally, there are five infinitely-recurring prime patterns of length 3. These are "ccc" (three composites in a row), "ccp", "cpc", "pcc" and "pcp". Others, like "ppc", starting at 2, only occur a finite number of times.

Crossrefs

Cf. A023189, A035326.

Sequence in context: A060688 A005691 A035954 * A064480 A274111 A209000

Adjacent sequences: A023189 A023190 A023191 * A023193 A023194 A023195

Keyword

nonn

Author

David W. Wilson

Status

approved