A020329 Consider integers z such that C(z,4) = C(x,4) + C(y,4), x >= y >= 4, is solvable. Sequence gives values of z.

8, 200

Offset

1,1

Comments

a(3) > 126900. - Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), May 02 2000

a(3) > 1350000. - Sean A. Irvine, Apr 20 2019

References

A. S. Fraenkel, Diophantine equations involving generalized triangular and tetrahedral numbers, pp. 99-114 of A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory. Academic Press, NY, 1971.

Links

Table of n, a(n) for n=1..2.

H. Finner and K. Strassburger, Increasing sample sizes do not necessarily increase the power of UMPU-tests for 2 X 2-tables, Metrika, 54, 77-91, (2001).

Heiko Harborth, Fermat-like binomial equations, Applications of Fibonacci numbers, Proc. 2nd Int. Conf., San Jose/Ca., August 1986, 1-5 (1988).

J. Leech, Some solutions of Diophantine equations, Proc. Camb. Phil. Soc., 53 (1957), 778-780.

M. Wunderlich, Certain properties of pyramidal and figurate numbers, Math. Comp., 16 (1962), 482-486.

Mathematica

nn = 1000; t = Binomial[Range[nn], 4]; d = Intersection[t, Union[Flatten[Table[t[[i]] + t[[j]], {i, 4, nn}, {j, i, nn}]]]]; Flatten[Table[Position[t, i], {i, d}]] (* T. D. Noe, Apr 02 2014 *)

Crossrefs

Cf. A010332.

Sequence in context: A024287 A208703 A304398 * A232518 A229265 A323562

Adjacent sequences: A020326 A020327 A020328 * A020330 A020331 A020332

Keyword

nonn,bref

Author

David W. Wilson

Extensions

Additional references from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Feb 09 2000

Status

approved