cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A133929 #21 Feb 16 2025 08:33:06
%S A133929 9,21,31,43,55,89
%N A133929 Positive integers that cannot be expressed using four pentagonal numbers.
%C A133929 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 A133929 Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section D3, Figurate numbers, pp. 222-228.
%H A133929 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentagonalNumber.html">Pentagonal Number</a>
%e A133929    9 =  5 +  1 + 1 + 1 + 1.
%e A133929   21 =  5 +  5 + 5 + 5 + 1.
%e A133929   31 = 12 + 12 + 5 + 1 + 1.
%e A133929   43 = 35 +  5 + 1 + 1 + 1.
%e A133929   55 = 51 +  1 + 1 + 1 + 1.
%e A133929   89 = 70 + 12 + 5 + 1 + 1.
%Y A133929 Cf. A000326, A007527, A100878.
%Y A133929 Equals A003679 \ A355660.
%K A133929 nonn,fini
%O A133929 1,1
%A A133929 _Eric W. Weisstein_, Sep 29 2007