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.
%I A068908 #21 Dec 20 2023 16:05:02 %S A068908 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 A068908 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 A068908 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 A068908 Number of partitions of n modulo 5. %C A068908 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 A068908 Henry Bottomley, <a href="http://www.se16.info/js/partitions.htm">Partition calculators using java applets</a> %H A068908 <a href="/index/Par#part">Index entries for sequences related to partitions</a> %F A068908 a(n) = A010874(A000041(n)) = A068906(5, n). %F A068908 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 A068908 Mod[PartitionsP[Range[0,110]],5] (* _Harvey P. Dale_, Dec 20 2023 *) %o A068908 (PARI) a(n) = numbpart(n) % 5; \\ _Michel Marcus_, Jul 14 2022 %Y A068908 Cf. A000041, A010874, A068906. %Y A068908 Cf. A040051, A068907, A068909, A020919. %K A068908 nonn %O A068908 0,3 %A A068908 _Henry Bottomley_, Mar 05 2002