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A039596 Numbers that are simultaneously triangular and square pyramidal. 7
1, 55, 91, 208335 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Equivalent to 1^2 + 2^2 + 3^2 + ... + r^2 = 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..4.

R. Finkelstein, 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

Cf. A000217, A000330, 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

STATUS

approved

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Last modified February 19 08:27 EST 2018. Contains 299330 sequences. (Running on oeis4.)