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A382244 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, n*a(n) is a triangular number (A000217).

%I A382244 #9 Mar 20 2025 09:28:48
%S A382244 0,1,3,2,7,9,6,4,15,5,12,21,10,25,27,8,31,33,35,37,39,11,24,45,22,13,
%T A382244 30,14,42,57,26,16,63,17,67,18,56,19,75,20,52,81,28,85,87,23,51,93,95,
%U A382244 97,99,46,40,105,60,90,36,29,66,117,54,121,69,32,127,84,58
%N A382244 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, n*a(n) is a triangular number (A000217).
%C A382244 A self-inverse permutation of the nonnegative integers.
%H A382244 Rémy Sigrist, <a href="/A382244/b382244.txt">Table of n, a(n) for n = 0..10000</a>
%H A382244 Rémy Sigrist, <a href="/A382244/a382244.gp.txt">PARI program</a>
%H A382244 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A382244 a(n) >= A061782(n) for any n > 0.
%e A382244 The initial terms are:
%e A382244   n   a(n)  n*a(n)
%e A382244   --  ----  -----------------
%e A382244    0     0    0 = A000217(0)
%e A382244    1     1    1 = A000217(1)
%e A382244    2     3    6 = A000217(3)
%e A382244    3     2    6 = A000217(3)
%e A382244    4     7   28 = A000217(7)
%e A382244    5     9   45 = A000217(9)
%e A382244    6     6   36 = A000217(8)
%e A382244    7     4   28 = A000217(7)
%e A382244    8    15  120 = A000217(15)
%e A382244    9     5   45 = A000217(9)
%e A382244   10    12  120 = A000217(15)
%e A382244   11    21  231 = A000217(21)
%e A382244   12    10  120 = A000217(15)
%e A382244   13    25  325 = A000217(25)
%e A382244   14    27  378 = A000217(27)
%e A382244   15     8  120 = A000217(15)
%o A382244 (PARI) \\ See Links section.
%Y A382244 Cf. A000217, A061782, A382244.
%K A382244 nonn
%O A382244 0,3
%A A382244 _Rémy Sigrist_, Mar 19 2025