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

1,2

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. 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

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: A006311 A344657 A224774 * A135457 A225505 A073733

Adjacent sequences: A034789 A034790 A034791 * A034793 A034794 A034795

Keyword

nonn

Author

David W. Wilson

Extensions

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

Status

approved