A381115 Composite terms in A381019 in order of appearance.

4, 9, 8, 6, 25, 12, 10, 49, 15, 16, 14, 27, 20, 21, 22, 18, 35, 24, 169, 28, 33, 26, 85, 32, 57, 77, 30, 34, 39, 55, 38, 51, 40, 91, 36, 121, 42, 65, 44, 45, 529, 48, 119, 46, 95, 81, 143, 50, 63, 52, 54, 115, 56, 841, 187, 69, 62, 125, 87, 64, 133, 75, 58, 221

Offset: 1

Author

N. J. A. Sloane, Feb 14 2025

Keywords

• nonn

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..336

Crossrefs

Cf. A381019, A381116, A381117.

Programs

Mathematica

nn = 500; c[_] = False; u = v = 2; a[1] = 1;
Monitor[Reap[
  Do[k = u;
    While[Or[c[k],
      ! CoprimeQ[k, Product[a[h], {h, n - Min[k, n - 1], n - 1}] ] ],
      If[k > n - 1, k = v, k++]];
    Set[{a[n], c[k]}, {k, True}];
    If[CompositeQ[k], Sow[k]];
    If[k == u, While[c[u], u++]];
If[k == v, While[Or[c[v], CompositeQ[v]], v++]], {n, 2, nn}] ][[-1, 1]], n] (* Michael De Vlieger, Feb 14 2025 *)

Python

from math import gcd
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    alst, aset, an, m = [1], {1}, 1, 2
    for n in count(2):
        if an > 3 and not isprime(an):
            yield an
        an = next(k for k in count(m) if k not in aset and all(gcd(alst[-j], k) == 1 for j in range(1, min(k, n-1)+1)))
        alst.append(an)
        aset.add(an)
        while m in aset: m += 1
print(list(islice(agen(), 64))) # Michael S. Branicky, Feb 14 2025