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%I #18 Mar 02 2019 11:53:53
%S 1,3,10,91,253,703,1711,1891,3403,5671,12403,15931,18721,25651,34453,
%T 38503,60031,73153,79003,88831,104653,108811,114481,126253,146611,
%U 158203,166753,171991,188191,218791,226801,258121,269011,286903,351541,371953,385003,392941
%N Lexicographically earliest sequence of pairwise coprime triangular numbers.
%C Previous name was: a(n) triangular, coprime to a(i), i < n.
%C Sierpinski proved that any finite set of pairwise coprime triangular numbers can be extended by adding an additional triangular number which is coprime to all the elements of the set. Therefore this sequence is infinite. - _Amiram Eldar_, Mar 01 2019
%D W. Sierpiński, 250 Problems in Elementary Number Theory. New York: American Elsevier, 1970, Problem 42.
%H Amiram Eldar, <a href="/A034792/b034792.txt">Table of n, a(n) for n = 1..10000</a>
%t t[n_] := n (n + 1)/2; s = {1}; While[Length[s] < 50, k = s[[-1]] + 1; While[Max[GCD[t[k], t /@ s]] > 1, k++]; AppendTo[s, k]]; t /@ s (* _Amiram Eldar_, Mar 01 2019 *)
%Y Cf. A000217, A076818.
%K nonn
%O 1,2
%A _David W. Wilson_
%E New name and more terms from _Amiram Eldar_, Mar 01 2019