A118367 Largest number that is not the sum of five n-gonal numbers.

0, 0, 0, 26, 47, 188, 245, 343, 494, 821, 901, 1283, 1729, 1972, 2715, 3795, 4030, 4788, 5681, 6379, 6948, 9484, 9913, 10342, 10771, 14064, 15035, 19182, 19865, 20548, 27315, 28194, 29073, 29952, 33351, 34302, 35253, 50772, 52106, 53440, 54774

Offset: 3

Author

T. D. Noe, Apr 25 2006

Keywords

• nonn

Comments

Legendre proved that a number N is the sum of five n-gonal numbers if N >= 28(n-2)^3. For odd n, four n-gonal numbers are enough. See A118368.

References

• Melvyn B. Nathanson, Additive number theory: the classical bases, Springer, 1996.

Links

• R. K. Guy, Every number is expressible as the sum of how many polygonal numbers?, Amer. Math. Monthly 101 (1994), 169-172.
• Eric Weisstein's World of Mathematics, Polygonal Number

Crossrefs

Cf. A118368.