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A278962 Each triple of consecutive terms contains a term that divides the product of the other two terms.

%I A278962 #11 Dec 02 2016 20:00:40
%S A278962 1,2,3,4,6,8,9,12,15,5,7,10,14,20,21,28,16,24,18,27,22,11,13,26,17,34,
%T A278962 19,38,23,46,25,50,29,58,30,45,32,36,40,48,35,42,49,54,63,56,64,70,80,
%U A278962 72,60,55,33,39,44,52,65,68,85,75,51,100,102,120,90,57,76
%N A278962 Each triple of consecutive terms contains a term that divides the product of the other two terms.
%C A278962 This is the lexicographically first sequence of distinct terms with this property.
%C A278962 Conjectures:
%C A278962 - All primes appear, and in increasing order,
%C A278962 - If a(i) is prime and i<j, then a(i) < a(j).
%C A278962 Here are some triples of consecutive terms where each term divides the product of the two others:
%C A278962 - (a(99), a(100), a(101)) = (132, 143, 156) = (2^2*3*11, 11*13, 2^2*3*13),
%C A278962 - (a(5714), a(5715), a(5716)) = (7055, 5146, 5270) = (5*17*83, 2*31*83, 2*5*17*31),
%C A278962 - (a(6674), a(6675), a(6676)) = (8099, 6052, 6188) = (7*13*89, 2^2*17*89, 2^2*7*13*17).
%H A278962 Rémy Sigrist, <a href="/A278962/b278962.txt">Table of n, a(n) for n = 1..10000</a>
%H A278962 Rémy Sigrist, <a href="/A278962/a278962.gp.txt">PARI program for A278962</a>
%K A278962 nonn
%O A278962 1,2
%A A278962 _Rémy Sigrist_, Dec 02 2016