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.

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

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[0]:= 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