OFFSET
1,2
COMMENTS
The m-th k-gonal number is 1 + k*m*(m-1)/2 - (m-1)^2 = A057145(k,m).
Numbers that are strictly trivially polygonal: numbers m that are only 2-gonal and m-gonal. - Daniel Mondot, Jun 13 2024
REFERENCES
Albert H. Beiler, Recreations In The Theory Of Numbers, The Queen Of Mathematics Entertains, Dover, NY, 1964, pp. 185-199.
LINKS
Michel Marcus, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
Eric Weisstein's World of Mathematics, Figurate Number.
FORMULA
An integer n >= 3 is in this sequence iff A176774(n) = n (or, equivalently, A176775(n) = 2). - Max Alekseyev, Apr 24 2018
EXAMPLE
3 is a triangular number, but is not a k-gonal number for any other k, so 3 is a term.
6 is both a triangular number and a hexagonal number, so 6 is not a term.
MATHEMATICA
Complement[ Table[i, {i, 300}], Take[ Union[ Flatten[ Table[1 + k*n(n - 1)/2 - (n - 1)^2, {n, 3, 40}, {k, 3, 300}]]], 300]]
PROG
(PARI) isok(n) = (n < 3) || (vecsum(vector(n-2, k, k+=2; ispolygonal(n, k))) == 1); \\ Michel Marcus, May 01 2016
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Robert G. Wilson v, Dec 01 2003
EXTENSIONS
Verified by Don Reble, Mar 12 2006
STATUS
approved