A027696 Nonparametric solutions to problem in A027669: k such that for some m >= 2, the sum of the first m k-gonal numbers is again a k-gonal number.

3, 4, 6, 8, 10, 11, 14, 17, 30, 41, 43, 50, 60, 88, 145, 276, 322, 374, 823, 1152

Offset

1,1

Comments

The parametric solution: if k==2 (mod 3) and k >= 5, the sum of the first (k^2-4*k-2)/3 k-gonal numbers is the ((k^3-6*k^2+3*k+19)/9)-th k-gonal number A057145(k,(k^3-6*k^2+3*k+19)/9) = A344410((k-2)/3).

2378, 2386, and 31265 are also terms. See link "Cannon Ball Numbers". - Pontus von Brömssen, Jan 08 2025

Links

Table of n, a(n) for n=1..20.

Brady Haran and Matt Parker, Cannon Ball Numbers, Numberphile (2019).

Crossrefs

Cf. A027669, A057145, A344410, A373711.

Sequence in context: A184398 A024665 A027669 * A027440 A360637 A169866

Adjacent sequences: A027693 A027694 A027695 * A027697 A027698 A027699

Keyword

nonn,more,changed

Author

Masanobu Kaneko (mkaneko(AT)math.kyushu-u.ac.jp)

Extensions

More terms from Masanobu Kaneko (mkaneko(AT)math.kyushu-u.ac.jp), Jan 05 1998

Status

approved