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

1,1

Comments

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.

Links

Table of n, a(n) for n=1..86.

Example

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.

Prog

(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, ", ")); ); }

Crossrefs

Cf. A177028, A177029, A342927, A342550.

Sequence in context: A202708 A027684 A276864 * A236442 A046537 A167596

Adjacent sequences: A342925 A342926 A342927 * A342929 A342930 A342931

Keyword

nonn

Author

Michel Marcus, Mar 29 2021

Status

approved