A378111 a(n) is the least prime p such that there are exactly n squarefree numbers strictly between p and the next prime, or -1 if there is no such p.

2, 5, 13, 31, 89, 139, 113, 199, 211, 317, 1759, 1381, 1951, 887, 4523, 2179, 2477, 4831, 5351, 4297, 1327, 9973, 14107, 19333, 16141, 20809, 15683, 37907, 28229, 58831, 31907, 19609, 25471, 40289, 114493, 43331, 44293, 34061, 191353, 31397, 107377, 134513, 186481, 448451, 175141, 332317, 188029

Offset: 0

Author

Robert Israel, Nov 29 2024

Keywords

• nonn

Comments

a(n) = A000040(k) where k is the least number such that A061398(k) = n.

Examples

			a(3) = 31 because there are 3 squarefree numbers between 31 and the next prime 37, namely 33, 34 and 35, and 31 is the least prime that works.
		

Links

• David A. Corneth, Table of n, a(n) for n = 0..253 (first 144 terms from Robert Israel)
• David A. Corneth, PARI program

Crossrefs

Cf. A000040, A005117, A061398, A377430.

Programs

Maple

V:= Array(0..100): count:= 0: q:= 2:
for k from 1 while count < 101 do
  p:= q; q:= nextprime(q);
  v:= nops(select(numtheory:-issqrfree,[$p+1 .. q-1]));
  if v <= 100 and V[v] = 0 then
    V[v]:= p; count:= count+1;
  fi
od: