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A133929 Positive integers that cannot be expressed using four pentagonal numbers. 2
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.

CROSSREFS

Cf. A000326, A007527, A100878.

Equals A003679 \ A355660.

Sequence in context: A173460 A110701 A243703 * A325573 A086470 A176256

Adjacent sequences:  A133926 A133927 A133928 * A133930 A133931 A133932

KEYWORD

nonn,fini

AUTHOR

Eric W. Weisstein, Sep 29 2007

STATUS

approved

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Last modified October 6 08:17 EDT 2022. Contains 357263 sequences. (Running on oeis4.)