OFFSET
1,1
COMMENTS
Richard Blecksmith & John Selfridge found 204 such integers among the first million, the largest of which is 33066. They believe that they have found them all (Richard K. Guy reference).
a(205) > 10^11, if it exists, from Giovanni Resta in A003679.
REFERENCES
Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section D3, Figurate numbers, pp. 222-228.
LINKS
Richard K. Guy, Every number is expressible as the sum of how many polygonal numbers?, Amer. Math. Monthly 101 (1994), 169-172.
FORMULA
A100878(a(n)) = 4.
EXAMPLE
4 = 1 + 1 + 1 + 1.
8 = 5 + 1 + 1 + 1.
16 = 5 + 5 + 5 + 1.
Also, it is not possible to get these terms when summing three or fewer pentagonal numbers.
MATHEMATICA
nn = 100;
pen = Table[n (3n - 1)/2, {n, 0, nn - 1}];
lst = Range[pen[[-1]]];
Do[n = pen[[i]]+pen[[j]]+pen[[k]]; If[n <= pen[[-1]], lst = DeleteCases[lst, n]], {i, 1, nn}, {j, i, nn}, {k, j, nn}];
A003679 = lst;
Complement[A003679, {9, 21, 31, 43, 55, 89}] (* Jean-François Alcover, Jul 13 2022, after T. D. Noe in A003679 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Jul 12 2022
STATUS
approved