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A216269
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Numbers n such that n^2 - 1 is a tetrahedral number (A000292).
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2
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OFFSET
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1,2
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COMMENTS
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Corresponding tetrahedral numbers are in A216268.
The curve 6*(x^2-1)-y*(y+1)*(y+2)=0 is elliptic, and has finitely many integral points by Siegel's theorem. - Robert Israel, Apr 22 2021
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LINKS
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MATHEMATICA
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t = {}; Do[tet = n (n + 1) (n + 2)/6; If[IntegerQ[s = Sqrt[tet + 1]], AppendTo[t, s]], {n, 0, 100000}]; t (* T. D. Noe, Mar 18 2013 *)
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PROG
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(Python)
import math
for i in range(1L<<30):
t = i*(i+1)*(i+2)/6 + 1
sr = int(math.sqrt(t))
if sr*sr == t:
print sr,
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CROSSREFS
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Cf. A003556 (both square and tetrahedral).
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KEYWORD
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nonn,fini
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AUTHOR
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STATUS
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approved
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