A133929 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A133929

Positive integers that cannot be expressed using four pentagonal numbers.

9, 21, 31, 43, 55, 89

(list; graph; refs; listen; history; text; internal format)

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. 222-228.

LINKS

Table of n, a(n) for n=1..6.

Eric Weisstein's World of Mathematics, Pentagonal Number

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.