

A342928


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


1



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
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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 3gonal and 6gonal number; it is the 3rd triangular number so a(1) = 3.
9 is A177029(2); it is a 4gonal and 9gonal 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/k4+2*k)/(k1)); 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



