A309108 Lexicographically earliest sequence such that the product a(j)*a(j+k)*a(j+2k) for any j and k is a unique positive integer.

1, 1, 1, 2, 3, 2, 5, 6, 7, 4, 10, 9, 7, 11, 12, 8, 13, 11, 17, 19, 15, 23, 7, 14, 16, 12, 27, 13, 25, 29, 31, 37, 33, 30, 26, 16, 20, 27, 34, 29, 35, 18, 41, 43, 47, 53, 39, 37, 49, 51, 59, 38, 40, 41, 46, 47, 42, 19, 31, 44, 55, 56, 61, 57, 67, 64, 45, 71, 62

Offset: 0

Author

Aaron Kemats, Sep 03 2019

Keywords

• nonn

Comments

This sequence has an infinite number of terms. The upper bound for any term n > 3 is prime(n-3).

Examples

			a(4)*a(7)*a(10) = 3*6*10 = 180. These are the only three equally-spaced terms whose product comes out to be 180.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..1000
• Rémy Sigrist, PARI program for A309108

Programs

PARI

\\ See Links section.

Extensions

Data corrected and incorrect program removed by Rémy Sigrist, Apr 10 2021