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A307174
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Numbers that are both triangular and icosahedral.
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1
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OFFSET
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1,3
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COMMENTS
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Similar to the list of triangular and tetrahedral numbers (A027568). It would appear that the similar sequence of pentagonal-dodecahedral numbers contains only the trivial cases of 0 and 1.
Terms n*(n+1)/2 = m*(5*m^2-5*m+2)/2 corresponds to integral points (X,Y) = (5*m,5*n) on the elliptic curve Y^2 + Y = X^3 - 5*X^2 + 10*X, which can be computed efficiently. There are none besides those already listed. - Max Alekseyev, Feb 12 2024
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LINKS
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MATHEMATICA
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Intersection[Accumulate[Range[0, 199]], Table[n (5n^2 - 5n + 2)/2, {n, 0, 99}]] (* Alonso del Arte, Jul 10 2019 *)
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PROG
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(PARI) lista(nn) = for (n=0, nn, if (ispolygonal(k=n*(5*n^2 - 5*n + 2)/2, 3), print1(k, ", "))); \\ Michel Marcus, Jul 10 2019
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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