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A381115 Composite terms in A381019 in order of appearance.

%I A381115 #16 Feb 15 2025 14:11:57
%S A381115 4,9,8,6,25,12,10,49,15,16,14,27,20,21,22,18,35,24,169,28,33,26,85,32,
%T A381115 57,77,30,34,39,55,38,51,40,91,36,121,42,65,44,45,529,48,119,46,95,81,
%U A381115 143,50,63,52,54,115,56,841,187,69,62,125,87,64,133,75,58,221
%N A381115 Composite terms in A381019 in order of appearance.
%H A381115 Michael S. Branicky, <a href="/A381115/b381115.txt">Table of n, a(n) for n = 1..336</a>
%t A381115 nn = 500; c[_] = False; u = v = 2; a[1] = 1;
%t A381115 Monitor[Reap[
%t A381115   Do[k = u;
%t A381115     While[Or[c[k],
%t A381115       ! CoprimeQ[k, Product[a[h], {h, n - Min[k, n - 1], n - 1}] ] ],
%t A381115       If[k > n - 1, k = v, k++]];
%t A381115     Set[{a[n], c[k]}, {k, True}];
%t A381115     If[CompositeQ[k], Sow[k]];
%t A381115     If[k == u, While[c[u], u++]];
%t A381115 If[k == v, While[Or[c[v], CompositeQ[v]], v++]], {n, 2, nn}] ][[-1, 1]], n] (* _Michael De Vlieger_, Feb 14 2025 *)
%o A381115 (Python)
%o A381115 from math import gcd
%o A381115 from sympy import isprime
%o A381115 from itertools import count, islice
%o A381115 def agen(): # generator of terms
%o A381115     alst, aset, an, m = [1], {1}, 1, 2
%o A381115     for n in count(2):
%o A381115         if an > 3 and not isprime(an):
%o A381115             yield an
%o A381115         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)))
%o A381115         alst.append(an)
%o A381115         aset.add(an)
%o A381115         while m in aset: m += 1
%o A381115 print(list(islice(agen(), 64))) # _Michael S. Branicky_, Feb 14 2025
%Y A381115 Cf. A381019, A381116, A381117.
%K A381115 nonn
%O A381115 1,1
%A A381115 _N. J. A. Sloane_, Feb 14 2025