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

1,1

Links

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

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 *)

Prog

(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

Crossrefs

Cf. A381019, A381116, A381117.

Sequence in context: A371500 A197580 A081382 * A188658 A248803 A376152

Adjacent sequences: A381110 A381111 A381113 * A381116 A381117 A381118

Keyword

nonn,new

Author

N. J. A. Sloane, Feb 14 2025

Status

approved