A184762 The number of numbers k > n such that Sum_{i=n..k} i^2 is a square.

1, 0, 3, 0, 0, 0, 5, 0, 2, 0, 1, 0, 1, 0, 2, 0, 2, 1, 0, 4, 1, 2, 0, 0, 7, 0, 2, 2, 0, 1, 0, 4, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,3

Comments

It is an old result (see Watson) that for n=1 the only k>n is k=24. Bremner, Stroeker, and Tzanakis compute the k for n <= 100 by solving elliptic curves. This sequence lists the number of k for each n; the values of k are in A184763. Sequence A180442 lists the n for which a(n) is nonzero.

Links

Table of n, a(n) for n=1..100.

A. Bremner, R. J. Stroeker, N. Tzanakis, On Sums of Consecutive Squares, J. Number Theory 62 (1997), 39-70.

G. N. Watson, The problem of the square pyramid, Messenger of Mathematics 48 (1918), pp. 1-22.

Crossrefs

Cf. A075404, A075405, A075406.

Sequence in context: A118112 A245552 A195938 * A330734 A081805 A333784

Adjacent sequences: A184759 A184760 A184761 * A184763 A184764 A184765

Keyword

nonn,hard

Author

T. D. Noe, Jan 21 2011

Status

approved