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A333531 Make a list of triples [n,k,m] with n>=1, k>=1, and T_n+T_k = T_m as in A309507, arranged in lexicographic order; sequence gives values of m.

%I A333531 #13 Apr 25 2021 13:12:18
%S A333531 3,6,10,6,8,15,8,11,21,28,13,36,10,11,16,23,45,13,28,55,18,23,66,21,
%T A333531 27,78,16,46,91,15,18,20,23,36,53,105,26,41,120,136,21,28,52,77,153,
%U A333531 23,31,58,86,171,40,49,190,21,23,33,44,54,71,210,23,26,36,41,78,116,231,28,253
%N A333531 Make a list of triples [n,k,m] with n>=1, k>=1, and T_n+T_k = T_m as in A309507, arranged in lexicographic order; sequence gives values of m.
%H A333531 J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, <a href="http://arxiv.org/abs/2004.14000">Three Cousins of Recaman's Sequence</a>, arXiv:2004:14000 [math.NT], April 2020.
%e A333531 The first few triples are:
%e A333531 2, 2, 3
%e A333531 3, 5, 6
%e A333531 4, 9, 10
%e A333531 5, 3, 6
%e A333531 5, 6, 8
%e A333531 5, 14, 15
%e A333531 6, 5, 8
%e A333531 6, 9, 11
%e A333531 6, 20, 21
%e A333531 7, 27, 28
%e A333531 8, 10, 13
%e A333531 8, 35, 36
%e A333531 9, 4, 10
%e A333531 9, 6, 11
%e A333531 9, 13, 16
%e A333531 9, 21, 23
%e A333531 9, 44, 45
%e A333531 10, 8, 13
%e A333531 10, 26, 28
%e A333531 10, 54, 55
%e A333531 11, 14, 18
%e A333531 11, 20, 23
%e A333531 11, 65, 66
%e A333531 12, 17, 21
%e A333531 12, 24, 27
%e A333531 12, 77, 78
%e A333531 ...
%p A333531 # This program produces the triples for each value of n, but then they need to be sorted on k:
%p A333531 with(numtheory):
%p A333531 A:=[]; M:=100;
%p A333531 for n from 1 to M do
%p A333531 TT:=n*(n+1);
%p A333531 dlis:=divisors(TT);
%p A333531 for d in dlis do
%p A333531 if (d mod 2) = 1 then e := TT/d;
%p A333531 mi:=min(d,e); ma:=max(d,e);
%p A333531 k:=(ma-mi-1)/2;
%p A333531 m:=(ma+mi-1)/2;
%p A333531 # skip if k=0
%p A333531 if k>0 then
%p A333531 lprint(n,k,m);
%p A333531 fi;
%p A333531 fi;
%p A333531 od:
%p A333531 od:
%Y A333531 Cf. A000217, A309507, A333529, A333530.
%Y A333531 If we only take triples [n,k,m] with n <= k <= m, the values of k and m are A198455 and A198456 respectively.
%K A333531 nonn
%O A333531 1,1
%A A333531 _N. J. A. Sloane_, Apr 01 2020