A374351 - OEIS

%I #48 Aug 19 2024 22:01:51

%S 1,2,3,5,4,6,9,25,8,12,15,7,14,30,11,49,60,10,77,21,20,16,27,35,22,18,

%T 105,55,26,42,165,13,28,330,33,91,40,66,63,65,44,84,45,121,56,75,81,

%U 32,50,135,147,64,80,189,99,100,70,231,39,130,154,51,195,308,17,585,462,34,325,693

%N Lexicographically earliest infinite sequence of distinct positive integers such that for any triple i,j,k of consecutive terms, gcd(i,k) = 1 and A007947(i*j*k) is a term in A002110.

%C In other words a(n) is least k such that (k, a(n-2)) = 1 and rad(a(n-2)*a(n-1)*k) is a primorial number (alternatively i*j*k is in A055932).

%C Conjectures: A permutation of the positive integers, a(n) = prime p (> 2) iff p is least unused odd term, 2|i, and rad(i*j) is a primorial number divisible by all primes < p but not by p; primes appear in natural order.

%H Dominic McCarty, <a href="/A374351/b374351.txt">Table of n, a(n) for n = 1..10000</a>

%H Dominic McCarty, <a href="/A374351/a374351_1.txt">Java program for A374351</a>

%e a(1,2,3) = 1,2,3 the lexicographically earliest triple of numbers satisfying the definition: 3 and 1 are coprime whilst 1*2*3 = 6 = A002110(2).

%e a(4) = 5 because (2,5) = 1 and 2*3*5 = 30 = A002110(3).

%e a(9,10,11) = 8,12,15 and 7 is the smallest novel number prime to 12 and rad(12*15*7) = 210 = A002110(4).

%o (Java) See Dominic McCarty link.

%Y Cf. A002110, A007947, A055932, A374445.

%K nonn

%O 1,2

%A _David James Sycamore_, Jul 09 2024

%E More terms from _Dominic McCarty_, Aug 19 2024