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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 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.)