

A133929


Positive integers that cannot be expressed using four pentagonal numbers.


2




OFFSET

1,1


COMMENTS

Equivalently, integers m such that the smallest number of pentagonal numbers (A000326) which sum to m is exactly five, that is, A100878(a(n)) = 5. Richard Blecksmith & John Selfridge found these six integers among the first million, they believe that they have found them all (Richard K. Guy reference).  Bernard Schott, Jul 22 2022


REFERENCES

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


LINKS



EXAMPLE

9 = 5 + 1 + 1 + 1 + 1.
21 = 5 + 5 + 5 + 5 + 1.
31 = 12 + 12 + 5 + 1 + 1.
43 = 35 + 5 + 1 + 1 + 1.
55 = 51 + 1 + 1 + 1 + 1.
89 = 70 + 12 + 5 + 1 + 1.


CROSSREFS



KEYWORD

nonn,fini


AUTHOR



STATUS

approved



