A342928 - OEIS

%I #8 Mar 29 2021 11:29:13

%S 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 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 3,3,4,3,3,4,5,3,3,4,5,3,4,3,4,5,7,3,4

%N The smallest polygonal index of numbers that have exactly two different representations as polygonal numbers (A177029).

%C 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 6 is A177029(1); it is a 3-gonal and 6-gonal number; it is the 3rd triangular number so a(1) = 3.

%e 9 is A177029(2); it is a 4-gonal and 9-gonal number; it is the 3rd square number so a(2) = 3.

%o (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 lista(nn) = {for (n=3, nn, my(r = row(n)); if (#r == 2, my(k); ispolygonal(n, r[1], &k); print1(k, ", ")););}

%Y Cf. A177028, A177029, A342927, A342550.

%K nonn

%O 1,1

%A _Michel Marcus_, Mar 29 2021