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 A034792 Lexicographically earliest sequence of pairwise coprime triangular numbers. 2
 1, 3, 10, 91, 253, 703, 1711, 1891, 3403, 5671, 12403, 15931, 18721, 25651, 34453, 38503, 60031, 73153, 79003, 88831, 104653, 108811, 114481, 126253, 146611, 158203, 166753, 171991, 188191, 218791, 226801, 258121, 269011, 286903, 351541, 371953, 385003, 392941 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Previous name was: a(n) triangular, coprime to a(i), i < n. 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 REFERENCES W. SierpiĆski, 250 Problems in Elementary Number Theory. New York: American Elsevier, 1970, Problem 42. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 MATHEMATICA 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 *) CROSSREFS Cf. A000217, A076818. Sequence in context: A136505 A006311 A224774 * A135457 A225505 A073733 Adjacent sequences:  A034789 A034790 A034791 * A034793 A034794 A034795 KEYWORD nonn AUTHOR EXTENSIONS New name and more terms from Amiram Eldar, Mar 01 2019 STATUS approved

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Last modified September 25 06:32 EDT 2020. Contains 337335 sequences. (Running on oeis4.)