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A374351
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.
2
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, 105, 55, 26, 42, 165, 13, 28, 330, 33, 91, 40, 66, 63, 65, 44, 84, 45, 121, 56, 75, 81, 32, 50, 135, 147, 64, 80, 189, 99, 100, 70, 231, 39, 130, 154, 51, 195, 308, 17, 585, 462, 34, 325, 693
OFFSET
1,2
COMMENTS
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).
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.
LINKS
EXAMPLE
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).
a(4) = 5 because (2,5) = 1 and 2*3*5 = 30 = A002110(3).
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).
PROG
(Java) See Dominic McCarty link.
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Dominic McCarty, Aug 19 2024
STATUS
approved