%I
%S 2,3,5,7,13,19,61,211,151,181,199,113,1069,1129,773,3137,887,13187,
%T 14087,5351,29881,2477,30727,69263,40289,35677,118973,110359,31397,
%U 186481,294563,155921,404851,221327,332317,265621,1665343,544279,1349533,2124679,1242643,3826019,7230331,1444309,5831401
%N a(n) is the first prime p such that each of the first n primes divides at least one of the composites between p and the next prime, but prime(n+1) does not divide any of these.
%C a(n) >= A341650(n), with equality if and only if A341650(n) < A341650(n+1).
%H Robert Israel, <a href="/A341640/b341640.txt">Table of n, a(n) for n = 0..78</a>
%e a(7) = 211 because each of the first 7 primes divides at least one of the composites 212 to 222 (2212, 3213, 5215, 7217, 11220, 13221, 17221), but the 8th prime 19 does not.
%p N:= 50: # for a(0) to a(N)
%p count:= 1:
%p P:= [seq(ithprime(i),i=1..N)]:
%p V:= Array(0..N): V[0]:= 2: q:= 3:
%p while count < N+1 do
%p p:= q; q:= nextprime(p);
%p for r from 1 to N do x:= p mod P[r]; if subs(0=P[r],x) >= qp then break fi od;
%p r:= r1;
%p if r <= N and V[r] = 0 then V[r]:= p; count:= count+1; fi;
%p od:
%p convert(V,list);
%Y Cf. A341650.
%K nonn
%O 0,1
%A _J. M. Bergot_ and _Robert Israel_, Feb 18 2021
