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A110375 Numbers n such that Maple 9.5, Maple 10, Maple 11 and Maple 12 give the wrong answers for the number of partitions of n.

%I A110375 #17 Aug 21 2024 05:36:47
%S A110375 11269,11566,12376,12430,12700,12754,15013,17589,17797,18181,18421,
%T A110375 18453,18549,18597,18885,18949,18997,20865,21531,21721,21963,22683,
%U A110375 23421,23457,23547,23691,23729,23853,24015,24087,24231,24339,24519,24591,24627,24681,24825,24933,25005,25023,25059,25185,25293,27020
%N A110375 Numbers n such that Maple 9.5, Maple 10, Maple 11 and Maple 12 give the wrong answers for the number of partitions of n.
%C A110375 Based on various postings on the Web, sent to _N. J. A. Sloane_ by _R. J. Mathar_. Thanks to several correspondents who sent information about other versions of Maple.
%C A110375 Mathematica 6.0, DrScheme and PARI 2.3.3 all give the correct answers.
%C A110375 Ramanujan's congruence says that numbpart(5*k+4) == 0 (mod 5), so numbpart(11269) = ...851 == 1 (mod 5) can't be correct. - _Robert Gerbicz_, May 13 2008
%H A110375 Alec Mihailovs and others, <a href="https://www.mapleprimes.com/posts/39381-A110375">Concerning this sequence</a>
%e A110375 From PARI, the correct answer:
%e A110375 numbpart(11269)
%e A110375 2311391772313039755144117876494556289590601993601099725578515191051551761\
%e A110375 80318215891795874905318274163248033071850
%e A110375 From Maple 11, incorrect:
%e A110375 combinat[numbpart](11269);
%e A110375 2311391772313039755144117876494556289590601993601099725578515191051551761\
%e A110375 80318215891795874905318274163248033071851
%e A110375 On the other hand, the old Maple 6 gives the correct answer.
%Y A110375 Cf. A000041.
%K A110375 nonn
%O A110375 1,1
%A A110375 _N. J. A. Sloane_, May 13 2008
%E A110375 More terms from _R. J. Mathar_, May 14 2008, based on a comparison of results from Maple 9 and PARI 2.3.3.