A386267 If k appears, k^2 does not.

2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81

Offset

1,1

Comments

4 = 2^2 is not included because 2 is already in this array.

k >= 2 is a term if and only if A007814(A052409(k)) is even. - Pontus von Brömssen, Jul 17 2025

This sequence has infinitely many terms that are squares, since if m is a term then m^(4^k) is also a term, for k > 0. - Gonzalo Martínez, Jul 18 2025

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Mathematica

s={}; Do[If[!MemberQ[s, Sqrt[k]], AppendTo[s, k]], {k, 2, 81}]; s (* James C. McMahon, Jul 17 2025 *)

Prog

(Ruby)
def A386267(n)
  i = 2
  ary = []
  while ary.size < n
    j = Math.sqrt(i).to_i
    if j * j != i || !ary.include?(j)
      ary << i
    end
    i += 1
  end
  ary
end
p A386267(100)

Crossrefs

Cf. A000037, A007814, A052409, A003159 (if k appears then 2k does not).

Sequence in context: A031975 A028729 A213367 * A175084 A171519 A072099

Adjacent sequences: A386264 A386265 A386266 * A386268 A386269 A386270

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 17 2025

Status

approved