cp's OEIS Frontend

A340802 Number of composite numbers between the largest noncomposite number <= n! and the smallest noncomposite number >= n!.

%I A340802 #20 Jan 29 2021 07:41:56
%S A340802 0,0,1,5,13,7,11,53,29,21,13,29,89,19,89,75,89,77,189,59,61,103,185,
%T A340802 203,189,95,43,167,253,107,187,79,37,289,173,257,97,43,169,135,131,
%U A340802 175,179,155,291,189,311,155,141,157,449,119,129,349,131,609,383,391,429
%N A340802 Number of composite numbers between the largest noncomposite number <= n! and the smallest noncomposite number >= n!.
%H A340802 Alois P. Heinz, <a href="/A340802/b340802.txt">Table of n, a(n) for n = 1..2000</a>
%F A340802 a(n) = A058054(n)-1 for n >= 2.
%F A340802 a(n) = A054588(n)-1 for n >= 3.
%F A340802 a(n) = 2 * A340013 - 1 for n >= 3.
%e A340802 a(4) = 5: 24, 25, 26, 27, 28.
%e A340802 a(5) = 13: 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126.
%e A340802 a(6) = 7: 720, 721, 722, 723, 724, 725, 726.
%p A340802 prevprime(2):= 1:
%p A340802 a:= n-> (f-> max(nextprime(f-1)-prevprime(f+1)-1, 0))(n!):
%p A340802 seq(a(n), n=1..64);
%t A340802 a[n_] := If[n<3, 0, NextPrime[n!] - NextPrime[n!, -1] - 1];
%t A340802 Array[a, 100] (* _Jean-François Alcover_, Jan 29 2021 *)
%Y A340802 Cf. A000040, A002808, A008578, A046933, A054588, A058054, A340013.
%K A340802 nonn
%O A340802 1,4
%A A340802 _Alois P. Heinz_, Jan 21 2021