%I #13 Aug 19 2024 02:38:18
%S 1,2,3,4,5,6,7,10,9,8,15,14,11,30,49,12,25,16,21,20,27,28,45,22,35,18,
%T 55,42,13,110,63,26,165,56,33,40,77,24,65,154,39,50,231,32,75,64,81,
%U 70,99,52,105,44,91,60,121,84,125,36,175,48,143,140,51,286
%N Lexicographically earliest infinite sequence of distinct positive integers having the property that for any triple i,j,k of consecutive terms gcd(j,k) = 1 whereas A007947(i*j*k) is a term in A002110.
%C In other words a(n) is least k such that (j,k) = 1 and rad(i*j*k) is a primorial number (alternatively i*j*k is a term in A055932).
%C Conjectured to be a permutation of the positive integers with primes in order.
%H Rémy Sigrist, <a href="/A374575/b374575.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A374575/a374575.gp.txt">PARI program</a>
%e Sequence starts with a(1,2,3) = {1,2,3} because this is the smallest consecutive triple of terms satisfying the definition ((2,3) = 1 and rad(1*2*3) = 6 = A002110(2)).
%e a(4) = 4 because (3,4) = 1, rad(2*3*4) = 6 = A002110(2), and 4 is the smallest unused number with this property.
%o (PARI) \\ See Links section.
%Y Cf. A002110, A007947, A055932.
%K nonn
%O 1,2
%A _David James Sycamore_, Jul 11 2024
%E More terms from _Rémy Sigrist_, Aug 19 2024