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%I #21 Dec 20 2023 16:05:02
%S 1,1,2,3,0,2,1,0,2,0,2,1,2,1,0,1,1,2,0,0,2,2,2,0,0,3,1,0,3,0,4,2,4,3,
%T 0,3,2,2,0,0,3,3,4,1,0,4,3,4,3,0,1,3,4,1,0,1,3,4,0,0,2,0,1,4,0,3,0,4,
%U 0,0,3,0,3,4,0,4,1,3,4,0,1,2,0,4,0,2,2,3,4,0,3,4,2,2,0,4,4,0,1,0,2,1,4,0,0
%N Number of partitions of n modulo 5.
%C Of the partitions of numbers from 1 to 100000: 36256 are 0, 15758 are 1, 16133 are 2, 16028 are 3 and 15825 are 4 modulo 5, largely because the number of partitions of 5m+4 is always a multiple of 5.
%H Henry Bottomley, <a href="http://www.se16.info/js/partitions.htm">Partition calculators using java applets</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = A010874(A000041(n)) = A068906(5, n).
%F a(n) = Pm(n,1) with Pm(n,k) = if k<n then (Pm(n-k,k) + Pm(n,k+1)) mod 5 else 0^(n*(k-n)). [_Reinhard Zumkeller_, Jun 09 2009]
%t Mod[PartitionsP[Range[0,110]],5] (* _Harvey P. Dale_, Dec 20 2023 *)
%o (PARI) a(n) = numbpart(n) % 5; \\ _Michel Marcus_, Jul 14 2022
%Y Cf. A000041, A010874, A068906.
%Y Cf. A040051, A068907, A068909, A020919.
%K nonn
%O 0,3
%A _Henry Bottomley_, Mar 05 2002