A003556 Numbers that are both square and tetrahedral.

0, 1, 4, 19600

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full

Comments

A. J. J. Meyl proved in 1878 that only 1, 4 and 19600 are both square and tetrahedral. See link. [Bernard Schott, Dec 23 2012]

Examples

			From _Bernard Schott_, Dec 23 2012: (Start)
If S(n) = n^2 and T(m) = m*(m+1)*(m+2)/6, then
-> S(1)= T(1) = 1;
-> S(2)= T(2) = 4;
-> S(140) = T(48) = 19600. (End)
		

References

• D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 600.
• D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 165 (Rev. ed. 1997).

Links

• M. Gardner, Letter to N. J. A. Sloane, circa Aug 11 1980, concerning A001110, A027568, A039596, etc.
• A. J. J. Meyl, Question 1194, Nouvelles Annales de Mathématiques, 2ème série, tome 17 (1878), p. 464-467.

Crossrefs

Intersection of A000290 and A000292.

Programs

Mathematica

Select[Rest[FoldList[Plus, 0, Rest[FoldList[Plus, 0, Range[50000]]]]], IntegerQ[Sqrt[ # ]]&]
Intersection[Binomial[# + 2, 3]&/@Range[0, 10000], Range[0,409000]^2] (* Harvey P. Dale, Feb 01 2011 *)