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

Author

David W. Wilson

Keywords

• nonn
• changed

Examples

			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.
		

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)

Crossrefs

Cf. A023189, A035326.

Formula

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