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 A193715 #11 Apr 04 2025 02:47:17
%S A193715 1,2,4,6,7,9,11,12,13,15,17,18,20,22,23,25,27,29,30,32,34,35,37,39,41,
%T A193715 42,44,46,47,49,51,52,54,56,58,59,61,63,64,66,68,70,71,73,75,76,78,80,
%U A193715 81,82,84,86,87,89,91,92,94,96,98,99,101,103,104,106,108
%N A193715 Positions of triangular numbers (A000217) in the union of squares and triangular numbers (A005214).
%H A193715 Reinhard Zumkeller, <a href="/A193715/b193715.txt">Table of n, a(n) for n = 1..10000</a>
%F A193715 A010054(A005214(a(n))) = 1.
%F A193715 a(n) ~ c * n, where c = 1 + sqrt(2)/2 = 1.707106... . - _Amiram Eldar_, Apr 04 2025
%t A193715 With[{max = 2500}, Position[Union[Join[Accumulate[Range[Floor[(Sqrt[8*max + 1] - 1)/2]]], Range[Floor[Sqrt[max]]]^2]], _?(IntegerQ[Sqrt[8*# + 1]] &)] // Flatten] (* _Amiram Eldar_, Apr 04 2025 *)
%o A193715 (Haskell)
%o A193715 import Data.List (elemIndex)
%o A193715 import Data.Maybe (fromJust)
%o A193715 a193715 n = a193715_list !! (n-1)
%o A193715 a193715_list =
%o A193715 map ((+ 1) . fromJust . (`elemIndex` a005214_list)) $ tail a000217_list
%Y A193715 Cf. A000217, A005214, A010054, A193714.
%K A193715 nonn
%O A193715 1,2
%A A193715 _Reinhard Zumkeller_, Aug 03 2011