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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 6 01:28 EST 2023. Contains 360091 sequences. (Running on oeis4.)