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

Offset

0,3

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

Links

Table of n, a(n) for n=0..41.

Similar work at Permissible Patterns.

Formula

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

Example

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

Crossrefs

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

Sequence in context: A079492 A267161 A173784 * A005690 A364378 A005779

Adjacent sequences: A094657 A094658 A094659 * A094661 A094662 A094663

Keyword

nonn

Author

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

Status

approved