A039596 Numbers that are simultaneously triangular and square pyramidal.

0, 1, 55, 91, 208335

Offset

1,3

Comments

Equivalent to 0^2 + 1^2 + 2^2 + 3^2 + ... + r^2 = 0 + 1 + 2 + 3 + ... + s = n for some r and s.

References

Joe Roberts, Lure of the Integers, page 245 (entry for 645).

David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, p. 108.

Links

Table of n, a(n) for n=1..5.

R. Finkelstein and H. London, On triangular numbers which are sums of consecutive squares, J. Number Theory 4 (1972), 455-462.

M. Gardner, Letter to N. J. A. Sloane, circa Aug 11 1980, concerning A001110, A027568, A039596, etc.

H. E. Thomas Jr., Problem 5634, Amer. Math. Monthly, 75 (1968), p. 1018.

Example

1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 1 + 2 + 3 + ... + 10 = 55, so 55 is in the sequence.

Crossrefs

Intersection of A000217 and A000330.

Cf. A053611, A053612.

Sequence in context: A063873 A063131 A128880 * A013543 A115377 A146145

Adjacent sequences: A039593 A039594 A039595 * A039597 A039598 A039599

Keyword

fini,nonn,full

Author

Felice Russo

Extensions

Additional comments from Jud McCranie, Mar 19 2000

Zero inserted by Daniel Mondot, Sep 07 2023

Status

approved