

A355660


Numbers m such that the smallest number of pentagonal numbers (A000326) which sum to m is exactly 4.


2



4, 8, 16, 19, 20, 26, 30, 33, 38, 42, 50, 54, 60, 65, 67, 77, 81, 84, 88, 90, 96, 99, 100, 101, 111, 112, 113, 120, 125, 131, 135, 138, 142, 154, 159, 160, 166, 170, 171, 183, 195, 204, 205, 207, 217, 224, 225, 226, 229, 230, 236, 240, 241, 243, 255, 265, 275, 277, 286, 306, 308, 345
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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).


REFERENCES

Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section D3, Figurate numbers, pp. 222228.


LINKS



FORMULA



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}];


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



