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 A375377 #10 Nov 19 2024 17:32:55
%S A375377 1,2,1,3,2,1,4,3,2,1,5,4,3,2,1,6,5,5,3,2,1,7,6,4,4,3,2,1,8,7,7,5,4,3,
%T A375377 2,1,9,8,6,6,5,4,3,2,1,10,9,8,7,7,5,4,3,3,1,11,10,10,8,6,6,6,4,2,2,1,
%U A375377 12,11,12,9,8,7,7,5,5,3,2,1,13,12,9,10,9,8,5,6,6,4,4,2,1
%N A375377 Square array read by antidiagonals: the n-th row is the inverse to the permutation given by the n-th row of A375376.
%H A375377 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>.
%e A375377 Array begins:
%e A375377 n=1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
%e A375377 n=2: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
%e A375377 n=3: 1, 2, 3, 5, 4, 7, 6, 8, 10, 12, 9, 11, 15, 16, 13, ...
%e A375377 n=4: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
%e A375377 n=5: 1, 2, 3, 4, 5, 7, 6, 8, 9, 12, 10, 13, 15, 17, 11, ...
%e A375377 n=6: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
%e A375377 n=7: 1, 2, 3, 4, 6, 7, 5, 10, 11, 8, 12, 14, 9, 13, 15, ...
%e A375377 n=8: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
%e A375377 n=9: 1, 3, 2, 5, 6, 8, 4, 7, 10, 13, 11, 14, 17, 18, 9, ...
%e A375377 n=10: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
%e A375377 n=11: 1, 2, 4, 3, 6, 8, 5, 9, 12, 10, 13, 17, 7, 11, 16, ...
%e A375377 n=12: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
%e A375377 n=13: 1, 2, 4, 3, 5, 8, 6, 10, 12, 9, 14, 15, 7, 11, 13, ...
%e A375377 n=14: 1, 2, 3, 4, 5, 7, 6, 9, 10, 8, 11, 12, 13, 14, 15, ...
%e A375377 n=15: 1, 2, 3, 5, 4, 7, 8, 11, 6, 12, 14, 17, 9, 15, 19, ...
%e A375377 For n = 7 = 2^0 + 2^1 + 2^2, the set S (defined in A375376) is {0+2, 1+2, 2+2} = {2, 3, 4}. The first power towers formed by 2's, 3's, and 4's, in colex order, together with their ranks (by magnitude) are:
%e A375377 k | power tower | rank T(7,k)
%e A375377 --+-------------+------------
%e A375377 1 | 2 = 2 | 1
%e A375377 2 | 3 = 3 | 2
%e A375377 3 | 4 = 4 | 3
%e A375377 4 | 2^2 = 4 | 4
%e A375377 5 | 3^2 = 9 | 6
%e A375377 6 | 4^2 = 16 | 7
%e A375377 7 | 2^3 = 8 | 5
%e A375377 8 | 3^3 = 27 | 10
%e A375377 9 | 4^3 = 64 | 11
%e A375377 10 | 2^4 = 16 | 8
%e A375377 11 | 3^4 = 81 | 12
%e A375377 12 | 4^4 = 256 | 14
%e A375377 13 | 2^2^2 = 16 | 9
%e A375377 14 | 3^2^2 = 81 | 13
%e A375377 15 | 4^2^2 = 256 | 15
%Y A375377 Cf. A375375 (3rd row), A375376 (the inverse permutation to each row).
%K A375377 nonn,tabl
%O A375377 1,2
%A A375377 _Pontus von Brömssen_, Aug 14 2024