A027595 Sequence satisfies T^2(a)=a, where T is defined below.

1, 2, 2, 4, 4, 6, 7, 11, 12, 16, 18, 25, 28, 36, 41, 53, 59, 73, 82, 102, 115, 138, 155, 186, 209, 246, 275, 324, 363, 420, 468, 541, 605, 691, 768, 877, 976, 1103, 1222, 1380, 1530, 1716, 1895, 2122, 2343, 2609, 2872, 3192, 3514, 3890, 4269, 4716, 5172, 5697

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• eigen

Comments

Georg Fischer observes that A027595 and A007212 appear to be identical - is this a theorem? - N. J. A. Sloane, Oct 17 2018

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

References

• S. Viswanath (student, Dept. Math, Indian Inst. Technology, Kanpur) A Note on Partition Eigensequences, preprint, Nov 15 1996.

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..250
• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210; arXiv:math/0205301 [math.CO], 2002.
• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
• N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, Part I, Part 2, Slides. (Mentions this sequence)

Crossrefs

Cf. A027595.

Formula

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.

A027595 = T(A027596). - Sean A. Irvine, Nov 10 2019

Extensions

More terms and offset corrected by Sean A. Irvine, Nov 10 2019