Maybe work out the first few terms and look it up somewhere?!! The OEIS has hundreds of sequences mentioning those words - for example, %N A001922 Numbers n such that 3*n^2-3*n+1 is both a square (A000290) and a centered hexagonal number (A003215). and %N A253475 Indices of centered square numbers (A001844) which are also centered hexagonal numbers (A003215). Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Tue, Apr 23, 2019 at 11:10 PM Dan Asimov <dasimov@earthlink.net> wrote:
Just happened to notice that in the centered hexagonal numbers
H_n = 1 + 6 T_n = 3n^2 + 3n + 1
we have H_7 = 13^2. Also H_0 = 1^2.
So I tried to find all such cases of
H_n = K^2,
but am not sure of the best way to proceed. Suggestions?
—Dan
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