

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

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



