A341650 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.

2, 3, 5, 7, 13, 19, 61, 113, 113, 113, 113, 113, 773, 773, 773, 887, 887, 2477, 2477, 2477, 2477, 2477, 30727, 31397, 31397, 31397, 31397, 31397, 31397, 155921, 155921, 155921, 221327, 221327, 265621, 265621, 544279, 544279, 1242643, 1242643, 1242643, 1444309, 1444309, 1444309, 1561919, 1561919

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..86

Example

a(6) = 61 because each of the first 6 primes 2,3,5,7,11,13 divides at least one of the composites 62 to 66: 2|62, 3|63, 5|65, 7|63, 11|66 and 13|65.

Maple

N:= 50: # for a(0) to a(N)
P:= [seq(ithprime(i), i=1..N)]:
V:= Array(0..N): V[0]:= 2: q:= 3: m:= 0:
while m < N do
  p:= q; q:= nextprime(p);
  E:= mul(i, i=p+1..q-1);
  for r from 1 to N do if E mod P[r] <> 0 then break fi od;
r:= r-1;
  if r > m then
    for s from m+1 to r do V[s]:= p od;
    m:= r;
  fi;
od:
convert(V, list);

Crossrefs

Sequence in context: A330383 A146999 A147485 * A341640 A104189 A301776

Adjacent sequences: A341647 A341648 A341649 * A341651 A341652 A341653

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Feb 16 2021

Status

approved