A094660 - OEIS

%I #19 May 18 2024 15:04:46

%S 0,1,2,4,6,9,12,18,24,34,44,58,72,100,128,169,210,267,324,429,534,694,

%T 854,1064,1274,1657,2040,2571,3102,3780,4458,5801,7144,9067,10990,

%U 13472,15954,20356,24758,30607,36456,44280

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

%C 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

%H Similar work at <a href="http://www.opertech.com/primes/k-tuples.html">Permissible Patterns</a>.

%F a(n) = Sum_{k=1..floor((n+1)/2)} (n + 2 - 2*k)*A023189(k). - _Jon E. Schoenfield_, May 17 2024

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

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

%K nonn

%O 0,3

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