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

0,4

Comments

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

Links

Rémy Sigrist, Table of n, a(n) for n = 0..1000

Rémy Sigrist, PARI program for A309108

Example

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.

Prog

(PARI) See Links section.

Crossrefs

Sequence in context: A076685 A254503 A186646 * A308056 A336965 A293303

Adjacent sequences: A309105 A309106 A309107 * A309109 A309110 A309111

Keyword

nonn

Author

Aaron Kemats, Sep 03 2019

Extensions

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

Status

approved