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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.
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%I #67 Apr 10 2021 17:00:31

%S 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,

%T 13,25,29,31,37,33,30,26,16,20,27,34,29,35,18,41,43,47,53,39,37,49,51,

%U 59,38,40,41,46,47,42,19,31,44,55,56,61,57,67,64,45,71,62

%N 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.

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

%H Rémy Sigrist, <a href="/A309108/b309108.txt">Table of n, a(n) for n = 0..1000</a>

%H Rémy Sigrist, <a href="/A309108/a309108.gp.txt">PARI program for A309108</a>

%e 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.

%o (PARI) See Links section.

%K nonn

%O 0,4

%A _Aaron Kemats_, Sep 03 2019

%E Data corrected and incorrect program removed by _Rémy Sigrist_, Apr 10 2021