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

0,1

Comments

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

Links

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

David A. Corneth, PARI program

Example

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.

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:

Crossrefs

Cf. A000040, A005117, A061398, A377430.

Sequence in context: A200772 A099515 A056367 * A082733 A095134 A086758

Adjacent sequences: A378108 A378109 A378110 * A378112 A378113 A378114

Keyword

nonn

Author

Robert Israel, Nov 29 2024

Status

approved