cp's OEIS Frontend

A333530 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 k.

%I A333530 #20 Apr 25 2021 13:11:58
%S A333530 2,5,9,3,6,14,5,9,20,27,10,35,4,6,13,21,44,8,26,54,14,20,65,17,24,77,
%T A333530 9,44,90,5,11,14,18,33,51,104,21,38,119,135,12,22,49,75,152,14,25,55,
%U A333530 84,170,35,45,189,6,11,26,39,50,68,209,9,15,29,35,75,114,230,17,252
%N A333530 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 k.
%H A333530 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 A333530 The first few triples are:
%e A333530 2, 2, 3
%e A333530 3, 5, 6
%e A333530 4, 9, 10
%e A333530 5, 3, 6
%e A333530 5, 6, 8
%e A333530 5, 14, 15
%e A333530 6, 5, 8
%e A333530 6, 9, 11
%e A333530 6, 20, 21
%e A333530 7, 27, 28
%e A333530 8, 10, 13
%e A333530 8, 35, 36
%e A333530 9, 4, 10
%e A333530 9, 6, 11
%e A333530 9, 13, 16
%e A333530 9, 21, 23
%e A333530 9, 44, 45
%e A333530 10, 8, 13
%e A333530 10, 26, 28
%e A333530 10, 54, 55
%e A333530 11, 14, 18
%e A333530 11, 20, 23
%e A333530 11, 65, 66
%e A333530 12, 17, 21
%e A333530 12, 24, 27
%e A333530 12, 77, 78
%e A333530 ...
%p A333530 # This program produces the triples for each value of n, but then they need to be sorted on k:
%p A333530 with(numtheory):
%p A333530 A:=[]; M:=100;
%p A333530 for n from 1 to M do
%p A333530 TT:=n*(n+1);
%p A333530 dlis:=divisors(TT);
%p A333530   for d in dlis do
%p A333530 if (d mod 2) = 1 then e := TT/d;
%p A333530 mi:=min(d,e); ma:=max(d,e);
%p A333530 k:=(ma-mi-1)/2;
%p A333530 m:=(ma+mi-1)/2;
%p A333530 # skip if k=0
%p A333530     if k>0 then
%p A333530      lprint(n,k,m);
%p A333530     fi;
%p A333530 fi;
%p A333530 od:
%p A333530 od:
%Y A333530 Cf. A000217, A309507, A333529, A333531.
%Y A333530 If we only take triples [n,k,m] with n <= k <= m, the values of k and m are A198455 and A198456 respectively.
%K A333530 nonn
%O A333530 1,1
%A A333530 _N. J. A. Sloane_, Apr 01 2020