This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372718 #14 May 25 2024 15:23:54
%S A372718 3,5,33,39,95,105,189,203,315,333,473,495,663,689,885,915,1139,1173,
%T A372718 1425,1463,1743,1785,2093,2139,2475,2525,2889,2943,3335,3393,3813,
%U A372718 3875,4323,4389,4865,4935,5439,5513,6045,6123,6683,6765,7353,7439,8055,8145,8789,8883,9555,9653
%N A372718 Triangular numbers that are 2 mod 4, halved.
%C A372718 The sum of the first 2*a(n) numbers of any Fibonacci-like sequence equals its (a(n)+2)-nd term times the a(n)-th Lucas number.
%H A372718 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A372718 a(n) = A000217(A047457(n))/2 = A372070(n)/2.
%e A372718 10 is a triangular number that has a remainder of 2 when divided by 4. Therefore, its half, 5, is in this sequence. Moreover, the sum of the first 5*2 Fibonacci numbers is 143 (not counting zero). This sum is a product of 13, which is the (5+2 = 7)-th term of the Fibonacci sequence times 11, which is the fifth Lucas number.
%t A372718 Select[Table[n (n + 1)/2, {n, 200}], Mod[#, 4] == 2 &]/2
%Y A372718 Cf. A000032, A000045, A000217. A372048, A372049, A372050, A372051, A372070.
%K A372718 nonn,easy
%O A372718 1,1
%A A372718 _Tanya Khovanova_ and the PRIMES STEP senior group, May 11 2024