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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
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
Equals A003679 \ A355660.
Sequence in context: A173460 A110701 A243703 * A325573 A086470 A176256
KEYWORD
nonn,fini
AUTHOR
Eric W. Weisstein, Sep 29 2007
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)