A133929 - OEIS

A133929

Positive integers that cannot be expressed using four pentagonal numbers.

9, 21, 31, 43, 55, 89

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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.