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

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: A175107 A376685 A085181 * A268129 A185725 A359804

Adjacent sequences: A374348 A374349 A374350 * A374352 A374353 A374354

Keyword

nonn

Author

David James Sycamore, Jul 09 2024

Extensions

More terms from Dominic McCarty, Aug 19 2024

Status

approved