A133929 Positive integers that cannot be expressed using four pentagonal numbers.

9, 21, 31, 43, 55, 89

Offset: 1

Author

Eric W. Weisstein, Sep 29 2007

Keywords

• nonn
• fini

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

Examples

			   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.
		

References

• Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section D3, Figurate numbers, pp. 222-228.

Links

• Eric Weisstein's World of Mathematics, Pentagonal Number

Crossrefs

Cf. A000326, A007527, A100878.

Equals A003679 \ A355660.