A342928 The smallest polygonal index of numbers that have exactly two different representations as polygonal numbers (A177029).
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, 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, 3, 3, 4, 3, 3, 4, 5, 3, 3, 4, 5, 3, 4, 3, 4, 5, 7, 3, 4
Offset: 1
Keywords
Examples
6 is A177029(1); it is a 3-gonal and 6-gonal number; it is the 3rd triangular number so a(1) = 3. 9 is A177029(2); it is a 4-gonal and 9-gonal number; it is the 3rd square number so a(2) = 3.
Programs
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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 lista(nn) = {for (n=3, nn, my(r = row(n)); if (#r == 2, my(k); ispolygonal(n, r[1], &k); print1(k, ", ")););}
Comments