A034792 Lexicographically earliest sequence of pairwise coprime triangular numbers.

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

Author

David W. Wilson

Keywords

• nonn

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. Sierpiński, 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

Crossrefs

Cf. A000217, A076818.

Programs

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 *)

Extensions

New name and more terms from Amiram Eldar, Mar 01 2019