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 A373026 #16 Jun 11 2024 10:07:36 %S A373026 1,7,8,7,4,20,17,12,5,31,24,15,4,40,29,16,1,47,32,15,69,52,33,12,76, %T A373026 55,32,7,81,56,29,111,84,55,24,116,85,52,17,119,84,47,8,120,81,40,160, %U A373026 119,76,31,161,116,69,20,160,111,60,7,157,104,49,207,152,95,36,204,145,84,21,199,136,71 %N A373026 a(n) is the least positive integer k such that 3*n^2 + 2*n - k is a square. %C A373026 The scatterplot shows an interesting structure where terms are on descending hatches. %C A373026 Terms on each hatch are quite well fitted by a polynomial of degree 2. %C A373026 The parity of the term indices alternates from one hatch to the next and that of two consecutive terms alternates on the same hatch. %C A373026 For terms on a given hatch, the differences of order 2 quickly become constant and equal to 2. %C A373026 The fixed points begin 1, 16, 225, 3136, etc. They appear to be all squares and to come from A098301. %e A373026 a(1) = 1 because 3*1^2 + 2*1 = 5 and 5-1 is a square. So, 1 is a term. %e A373026 a(2) = 7 because 3*2^2 + 2*2 = 16 and 16-1, 16-2, 16-3, 16-4, 16-5, 16-6 are not squares, but 16-7 is. So, 7 is a term. %o A373026 (PARI) a(n) = my(m=3*n^2+2*n-1); m+1-sqrtint(m)^2; \\ _Michel Marcus_, May 20 2024 %Y A373026 Cf. A000005, A000290, A005408. %Y A373026 Cf. A373016, A373028. %K A373026 nonn,easy %O A373026 1,2 %A A373026 _Claude H. R. Dequatre_, May 20 2024