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 A341640 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. 1
 2, 3, 5, 7, 13, 19, 61, 211, 151, 181, 199, 113, 1069, 1129, 773, 3137, 887, 13187, 14087, 5351, 29881, 2477, 30727, 69263, 40289, 35677, 118973, 110359, 31397, 186481, 294563, 155921, 404851, 221327, 332317, 265621, 1665343, 544279, 1349533, 2124679, 1242643, 3826019, 7230331, 1444309, 5831401 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(n) >= A341650(n), with equality if and only if A341650(n) < A341650(n+1). LINKS Robert Israel, Table of n, a(n) for n = 0..78 EXAMPLE a(7) = 211 because each of the first 7 primes divides at least one of the composites 212 to 222 (2|212, 3|213, 5|215, 7|217, 11|220, 13|221, 17|221), but the 8th prime 19 does not. MAPLE N:= 50: # for a(0) to a(N) count:= 1: P:= [seq(ithprime(i), i=1..N)]: V:= Array(0..N): V:= 2: q:= 3: while count < N+1 do   p:= q; q:= nextprime(p);   for r from 1 to N do x:= -p mod P[r]; if subs(0=P[r], x) >= q-p then break fi od;   r:= r-1;   if r <= N and V[r] = 0 then V[r]:= p; count:= count+1;  fi; od: convert(V, list); CROSSREFS Cf. A341650. Sequence in context: A146999 A147485 A341650 * A104189 A301776 A178570 Adjacent sequences:  A341637 A341638 A341639 * A341641 A341642 A341643 KEYWORD nonn AUTHOR J. M. Bergot and Robert Israel, Feb 18 2021 STATUS approved

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Last modified December 1 22:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)