A094660 Number of permissible patterns of primes in a fixed interval of n consecutive integers.

0, 1, 2, 4, 6, 9, 12, 18, 24, 34, 44, 58, 72, 100, 128, 169, 210, 267, 324, 429, 534, 694, 854, 1064, 1274, 1657, 2040, 2571, 3102, 3780, 4458, 5801, 7144, 9067, 10990, 13472, 15954, 20356, 24758, 30607, 36456, 44280, 52104, 66168, 80232, 98524, 116816, 140797, 164778

Offset: 0

Author

Thomas J Engelsma (tom(AT)opertech.com), Jun 09 2004

Keywords

• nonn
• changed

Comments

Similar to A023192. (Here we ignore the empty pattern and start at 0.) These are called "admissible constellations" of primes. - Don Reble, Jun 12 2004

Examples

			a(5)=9 because primes can exist in interval as x.... .x... ..x.. ...x. ....x x.x.. .x.x. ..x.x or x...x
		

Links

• Similar work at Permissible Patterns.

Crossrefs

Cf. A008407, A020497, A023189. Equals A023192 - 1.

Formula

a(n) = Sum_{k=1..floor((n+1)/2)} (n + 2 - 2*k)*A023189(k). - Jon E. Schoenfield, May 17 2024

Extensions

a(42)-a(48) from Pontus von Brömssen, Aug 25 2025