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%I #20 Jul 28 2022 15:16:59
%S 9,21,31,43,55,89
%N Positive integers that cannot be expressed using four pentagonal numbers.
%C 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
%D Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section D3, Figurate numbers, pp. 222-228.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PentagonalNumber.html">Pentagonal Number</a>
%e 9 = 5 + 1 + 1 + 1 + 1.
%e 21 = 5 + 5 + 5 + 5 + 1.
%e 31 = 12 + 12 + 5 + 1 + 1.
%e 43 = 35 + 5 + 1 + 1 + 1.
%e 55 = 51 + 1 + 1 + 1 + 1.
%e 89 = 70 + 12 + 5 + 1 + 1.
%Y Cf. A000326, A007527, A100878.
%Y Equals A003679 \ A355660.
%K nonn,fini
%O 1,1
%A _Eric W. Weisstein_, Sep 29 2007
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