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 A027595 #25 Jul 08 2025 17:53:47 %S A027595 1,2,2,4,4,6,7,11,12,16,18,25,28,36,41,53,59,73,82,102,115,138,155, %T A027595 186,209,246,275,324,363,420,468,541,605,691,768,877,976,1103,1222, %U A027595 1380,1530,1716,1895,2122,2343,2609,2872,3192,3514,3890,4269,4716,5172,5697 %N A027595 Sequence satisfies T^2(a)=a, where T is defined below. %C A027595 _Georg Fischer_ observes that A027595 and A007212 appear to be identical - is this a theorem? - _N. J. A. Sloane_, Oct 17 2018 %C A027595 In reply to the above, no they are different, although the first difference probably does not occur until n=5935. The difference arises due to the handling of multiples of 5 in the respective transforms as explained in A027596. In particular, since A007213(50)=5936 while A027595(50)=5935, this sequence will differ from A007212 at n=5935. - _Sean A. Irvine_, Nov 10 2019 %D A027595 S. Viswanath (student, Dept. Math, Indian Inst. Technology, Kanpur) A Note on Partition Eigensequences, preprint, Nov 15 1996. %H A027595 Sean A. Irvine, <a href="/A027595/b027595.txt">Table of n, a(n) for n = 1..250</a> %H A027595 M. Bernstein and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210; arXiv:math/0205301 [math.CO], 2002. %H A027595 M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures] %H A027595 N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, <a href="https://vimeo.com/314786942">Part I</a>, <a href="https://vimeo.com/314790822">Part 2</a>, <a href="https://oeis.org/A320487/a320487.pdf">Slides.</a> (Mentions this sequence) %F A027595 Define T:a->b by: given a1<=a2<=..., let b(n) = number of ways of partitioning n into parts from a1, a2, ... such that parts = 0 mod 5 do not occur more than once. %F A027595 A027595 = T(A027596). - _Sean A. Irvine_, Nov 10 2019 %Y A027595 Cf. A027595. %K A027595 nonn,eigen %O A027595 1,2 %A A027595 _N. J. A. Sloane_ %E A027595 More terms and offset corrected by _Sean A. Irvine_, Nov 10 2019