cp's OEIS Frontend

A382245 Lexicographically earliest sequence of distinct nonnegative integers such that the product of two consecutive terms is always a triangular number (A000217).

%I A382245 #11 Mar 21 2025 02:31:20
%S A382245 0,1,3,2,5,9,4,7,13,6,11,21,10,12,23,45,14,15,8,17,33,16,31,61,30,26,
%T A382245 51,25,49,24,22,43,85,42,28,55,18,35,44,87,19,37,73,36,56,111,98,195,
%U A382245 62,69,34,39,20,41,81,40,52,103,205,66,58,115,57,29,59,117
%N A382245 Lexicographically earliest sequence of distinct nonnegative integers such that the product of two consecutive terms is always a triangular number (A000217).
%C A382245 This sequence has similarities with A026741: in both sequences, the product of two consecutive terms is always a triangular number; here all terms are distinct, there all products of two consecutive terms are distinct.
%H A382245 Rémy Sigrist, <a href="/A382245/b382245.txt">Table of n, a(n) for n = 0..10000</a>
%H A382245 Rémy Sigrist, <a href="/A382245/a382245.gp.txt">PARI program</a>
%e A382245 The initial terms are:
%e A382245   n   a(n)  a(n)*a(n+1)
%e A382245   --  ----  ------------------
%e A382245    0     0     0 = A000217(0)
%e A382245    1     1     3 = A000217(2)
%e A382245    2     3     6 = A000217(3)
%e A382245    3     2    10 = A000217(4)
%e A382245    4     5    45 = A000217(9)
%e A382245    5     9    36 = A000217(8)
%e A382245    6     4    28 = A000217(7)
%e A382245    7     7    91 = A000217(13)
%e A382245    8    13    78 = A000217(12)
%e A382245    9     6    66 = A000217(11)
%e A382245   10    11   231 = A000217(21)
%e A382245   11    21   210 = A000217(20)
%e A382245   12    10   120 = A000217(15)
%e A382245   13    12   276 = A000217(23)
%e A382245   14    23  1035 = A000217(45)
%e A382245   15    45   630 = A000217(35)
%o A382245 (PARI) \\ See Links section.
%Y A382245 Cf. A000217, A026741, A077220, A213005, A382244.
%K A382245 nonn
%O A382245 0,3
%A A382245 _Rémy Sigrist_, Mar 19 2025