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A130334 Smallest m>n such that the m-th and n-th triangular numbers are coprime.

%I A130334 #14 Feb 16 2025 08:33:06
%S A130334 2,4,10,6,7,10,9,10,13,12,13,22,15,16,22,18,19,22,21,22,25,24,25,37,
%T A130334 27,28,37,30,31,37,33,34,37,36,37,46,39,40,46,42,43,46,45,46,52,48,49,
%U A130334 58,51,52,58,54,55,58,57,58,61,60,61,73,63,64,73,66,67,70,69,70,73,72,73
%N A130334 Smallest m>n such that the m-th and n-th triangular numbers are coprime.
%H A130334 Reinhard Zumkeller, <a href="/A130334/b130334.txt">Table of n, a(n) for n = 1..10000</a>
%H A130334 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriangularNumber.html">Triangular Number</a>
%H A130334 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RelativelyPrime.html">Relatively Prime</a>
%F A130334 a(n) > n+1 for n>1; a(n) > n+2 for n with n mod 3 = 0;
%F A130334 a(n) = n + A130335(n).
%o A130334 (Python)
%o A130334 from math import gcd
%o A130334 def A130334(n):
%o A130334     k, Tn, Tm = n+1, n*(n+1)//2, (n+1)*(n+2)//2
%o A130334     while gcd(Tn,Tm) != 1:
%o A130334         k += 1
%o A130334         Tm += k
%o A130334     return k # _Chai Wah Wu_, Sep 16 2021
%Y A130334 Cf. A000217, A026741, A109007, A130335.
%K A130334 nonn
%O A130334 1,1
%A A130334 _Reinhard Zumkeller_, May 28 2007