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 A342928 #8 Mar 29 2021 11:29:13
%S A342928 3,3,4,3,4,3,4,3,5,3,3,3,4,5,3,4,3,4,3,7,4,3,3,4,3,3,5,3,3,4,4,3,5,3,
%T A342928 4,3,8,3,4,5,3,3,4,3,3,5,4,11,3,4,5,3,4,3,7,3,4,3,3,5,3,4,3,4,3,13,4,
%U A342928 3,3,4,3,3,4,5,3,3,4,5,3,4,3,4,5,7,3,4
%N A342928 The smallest polygonal index of numbers that have exactly two different representations as polygonal numbers (A177029).
%C A342928 By definition, a(n) can never be equal to 2. Up to 10^7, no n has been found with a(n) = 6, 10 or 16.
%e A342928 6 is A177029(1); it is a 3-gonal and 6-gonal number; it is the 3rd triangular number so a(1) = 3.
%e A342928 9 is A177029(2); it is a 4-gonal and 9-gonal number; it is the 3rd square number so a(2) = 3.
%o A342928 (PARI) row(n) = my(v=List()); fordiv(2*n, k, if(k<2, next); if(k==n, break); my(s=(2*n/k-4+2*k)/(k-1)); if(denominator(s)==1, listput(v, s))); Vecrev(v); \\ A177028
%o A342928 lista(nn) = {for (n=3, nn, my(r = row(n)); if (#r == 2, my(k); ispolygonal(n, r[1], &k); print1(k, ", ")););}
%Y A342928 Cf. A177028, A177029, A342927, A342550.
%K A342928 nonn
%O A342928 1,1
%A A342928 _Michel Marcus_, Mar 29 2021