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 A372341 #12 May 01 2024 11:30:00
%S A372341 1,2,4,3,5,7,6,8,11,16,9,12,17,22,29,10,13,18,23,30,37,14,19,24,31,38,
%T A372341 46,56,15,20,25,32,39,47,57,67,21,26,33,40,48,58,68,79,92,27,34,41,49,
%U A372341 59,69,80,93,106,121,28,35,42,50,60,70,81,94,107,122,137
%N A372341 Let F be the set of lattice points {(x, y) in N^2 | A005206(x) <= y <= A005206(x) + x}; order the points of F by ascending Y-coordinates and then by ascending X-coordinates; the n-th and a(n)-th points of F are arranged symmetrically with respect to the line x = y.
%C A372341 The set F is related to the "Quilt Tiling" described in Shectman's paper (see Links section) and has interesting properties: F is symmetrical with respect to the line x = y, for any n >= 0, there are n+1 points in F with a X-coordinate of n (or with a Y-coordinate of n).
%C A372341 This sequence is a self-inverse permutation of the positive integers with infinitely many fixed points (see A372231).
%H A372341 J. Parker Shectman, <a href="http://www.ootlinc.com/Fibonacci_Quilt_2_of_3_Cohorts_and_Numeration.pdf">A Quilt after Fibonacci, Part 2 of 3: Cohorts, Free Monoids, and Numeration</a>
%H A372341 Rémy Sigrist, <a href="/A372341/a372341.txt">C++ program</a>
%H A372341 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A372341 The elements of F with coordinates <= 10 are as follows:
%e A372341 | +-------------------+
%e A372341 10 | | 56 57 58 59 60|
%e A372341 | | |
%e A372341 9 | | 46 47 48 49 50|
%e A372341 | +---+ |
%e A372341 8 | | 37| 38 39 40 41 42|
%e A372341 | +---+---+ |
%e A372341 7 | | 29 30| 31 32 33 34 35|
%e A372341 | | | |
%e A372341 6 | | 22 23| 24 25 26 27 28|
%e A372341 | +---+-------+-------+---+-------+
%e A372341 5 | | 16 17 18| 19 20| 21|
%e A372341 | | | +---+
%e A372341 4 | | 11 12 13| 14 15|
%e A372341 | +---+ +-------+
%e A372341 3 | | 7| 8 9 10|
%e A372341 | +---+---+---+-------+
%e A372341 2 | | 4 5| 6|
%e A372341 | | +---+
%e A372341 1 | | 2 3|
%e A372341 +---+-------+
%e A372341 0 | 1|
%e A372341 ---+---+----------------------------------------
%e A372341 y/x| 0 1 2 3 4 5 6 7 8 9 10
%e A372341 So a(1) = 1, a(2) = 2, a(3) = 4, a(5) = 5, a(6) = 7, a(8) = 8, a(9) = 11, a(10) = 16, a(12) = 12, a(13) = 17, etc.
%o A372341 (C++) // See Links section.
%Y A372341 Cf. A005206, A345067, A372231 (fixed points).
%K A372341 nonn
%O A372341 1,2
%A A372341 _Rémy Sigrist_, Apr 28 2024