A374351 - OEIS

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.

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

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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

Dominic McCarty, Table of n, a(n) for n = 1..10000

Dominic McCarty, Java program for A374351

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

Cf. A002110, A007947, A055932, A374445.

Sequence in context: A185180 A175107 A085181 * A268129 A185725 A359804