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 A375376 #4 Aug 17 2024 13:57:27
%S A375376 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 A375376 2,1,9,8,6,6,5,4,3,2,1,10,9,8,7,7,5,4,3,3,1,11,10,11,8,6,6,7,4,2,2,1,
%U A375376 12,11,9,9,8,7,5,5,7,3,2,1,13,12,12,10,9,8,6,6,4,4,4,2,1
%N A375376 Square array read by antidiagonals: Let n = Sum_{i=1..m} 2^e_i be the binary expansion of n, let S be the set {e_i+2; 1 <= i <= m}, and let X be the sequence of power towers built of numbers in S, sorted first by their height and then colexicographically. The n-th row of the array gives the permutation of indices which reorders X by magnitude. In case of ties, keep the colexicographic order.
%C A375376 Each row is a permutation of the positive integers.
%C A375376 If n is a power of 2, the set S contains a single number and the n-th row is the identity permutation.
%H A375376 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>.
%e A375376 Array begins:
%e A375376 n=1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
%e A375376 n=2: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
%e A375376 n=3: 1, 2, 3, 5, 4, 7, 6, 8, 11, 9, 12, 10, 15, 16, 13, ...
%e A375376 n=4: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
%e A375376 n=5: 1, 2, 3, 4, 5, 7, 6, 8, 9, 11, 15, 10, 12, 16, 13, ...
%e A375376 n=6: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
%e A375376 n=7: 1, 2, 3, 4, 7, 5, 6, 10, 13, 8, 9, 11, 14, 12, 15, ...
%e A375376 n=8: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
%e A375376 n=9: 1, 3, 2, 7, 4, 5, 8, 6, 15, 9, 11, 16, 10, 12, 17, ...
%e A375376 n=10: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
%e A375376 n=11: 1, 2, 4, 3, 7, 5, 13, 6, 8, 10, 14, 9, 11, 22, 16, ...
%e A375376 n=12: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
%e A375376 n=13: 1, 2, 4, 3, 5, 7, 13, 6, 10, 8, 14, 9, 15, 11, 12, ...
%e A375376 n=14: 1, 2, 3, 4, 5, 7, 6, 10, 8, 9, 11, 12, 13, 14, 15, ...
%e A375376 n=15: 1, 2, 3, 5, 4, 9, 6, 7, 13, 21, 8, 10, 17, 11, 14, ...
%e A375376 For n = 7 = 2^0 + 2^1 + 2^2, the set S is {0+2, 1+2, 2+2} = {2, 3, 4}. The smallest power towers formed by 2's, 3's, and 4's, together with their colex ranks are:
%e A375376 k | power tower | colex rank T(7,k)
%e A375376 --+-------------+------------------
%e A375376 1 | 2 = 2 | 1
%e A375376 2 | 3 = 3 | 2
%e A375376 3 | 4 = 4 | 3
%e A375376 4 | 2^2 = 4 | 4
%e A375376 5 | 2^3 = 8 | 7
%e A375376 6 | 3^2 = 9 | 5
%e A375376 7 | 4^2 = 16 | 6
%e A375376 8 | 2^4 = 16 | 10
%e A375376 9 | 2^2^2 = 16 | 13
%e A375376 10 | 3^3 = 27 | 8
%e A375376 11 | 4^3 = 64 | 9
%e A375376 12 | 3^4 = 81 | 11
%e A375376 13 | 3^2^2 = 81 | 14
%e A375376 14 | 4^4 = 256 | 12
%e A375376 15 | 4^2^2 = 256 | 15
%Y A375376 Cf. A185969, A299229, A375374 (3rd row), A375377 (the inverse permutation to each row).
%K A375376 nonn,tabl
%O A375376 1,2
%A A375376 _Pontus von Brömssen_, Aug 14 2024