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A034792
Lexicographically earliest sequence of pairwise coprime triangular numbers.
3
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
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. SierpiƄski, 250 Problems in Elementary Number Theory. New York: American Elsevier, 1970, Problem 42.
LINKS
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
Sequence in context: A006311 A344657 A224774 * A135457 A225505 A073733
KEYWORD
nonn
EXTENSIONS
New name and more terms from Amiram Eldar, Mar 01 2019
STATUS
approved