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%I #24 Jul 20 2024 07:46:19
%S 1,2,3,4,9,8,15,14,45,16,27,10,21,20,63,40,81,32,75,28,135,56,165,98,
%T 225,64,105,22,315,44,525,88,735,128,243,50,147,80,189,100,231,130,
%U 693,160,441,110,273,220,567,200,729,70,33,140,99,280,297,350,363
%N Lexicographically earliest sequence of distinct positive integers such that any pair of consecutive terms are coprime whereas the squarefree kernel of their product is primorial.
%C In other words rad(a(n-2)*a(n-1)) is a term in A002110 whereas a(n-2) and a(n-1) share no common divisor > 1. Every term > a(1) = 1 is divisible by 2 or by 3 but not by both, and all terms other than 1,2,3 are composite.
%C {a(n); n >= 2} is conjectured to be a permutation of A047228.
%H Rémy Sigrist, <a href="/A374445/b374445.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A374445/a374445.gp.txt">PARI program</a>
%e The sequence starts with a(1) = 1, a(2) = 2 since (1,2) = 1 and 1*2 = A002110(1).
%e a(3) = 3 since (2,3) = 1 and 2*3 = 6 = A002110(2).
%t nn = 540; c[_] := False;
%t Array[Set[{a[#], c[#]}, {#, True}] &, 2]; j = a[2]; u = 3;
%t f[x_] := f[x] = Or[IntegerQ@ Log2[x], And[EvenQ[x], Union@ Differences@ PrimePi@ FactorInteger[x][[All, 1]] == {1}]];
%t Monitor[Do[k = u;
%t While[Or[! CoprimeQ[j, k], c[k], ! f[j*k]], k++];
%t Set[{a[n], c[k], j}, {k, True, k}];
%t If[k == u, While[c[u], u++]], {n, 3, nn}], n];
%t Array[a, nn] (* _Michael De Vlieger_, Jul 16 2024 *)
%o (PARI) \\ See Links section.
%Y Cf. A002110, A007947, A047228, A374351.
%K nonn
%O 1,2
%A _David James Sycamore_, Jul 08 2024
%E More terms from _Rémy Sigrist_, Jul 11 2024
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