A356190 a(n) is the least prime p such that there are exactly n primes strictly between p and 2*p, or -1 if there is no such p.

2, 7, 11, 17, 23, 29, 31, -1, 37, -1, 53, 61, 59, 71, 79, 89, -1, 109, 97, 101, -1, -1, 127, -1, 137, 151, 149, 157, -1, 179, -1, 191, -1, -1, 211, -1, -1, 223, 233, -1, 251, 257, 263, 293, -1, -1, -1, -1, 307, 311, -1, -1, -1, 331, 349, 347, 367, 373, 379, 389, 409, -1, -1, 419, -1, 431, 443

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..9999

Formula

a(n) <= A168421(n+1) - 2, with equality for n = 6, 263, 3061, 4750, 4893, 5029, 5555, 6101, ....

Example

a(3) = 11 because there are exactly 3 primes between 11 and 22, namely 13, 17 and 19, and 11 is the least prime that works.

Maple

V:= Vector(100, -1): p:= 1:
for n from 1 while p < 727 do # note that A168421(101) = 727
  p:= nextprime(p);
  v:= numtheory:-pi(2*p)-n;
  if v <= 100 and V[v] = -1 then
    V[v]:= p;
  fi
od:
convert(V, list);

Crossrefs

Cf. A168421.

Sequence in context: A090613 A063097 A297469 * A168421 A038942 A175283

Adjacent sequences: A356187 A356188 A356189 * A356191 A356192 A356193

Keyword

sign

Author

J. M. Bergot and Robert Israel, Jul 29 2022

Status

approved