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 A321902 #14 Feb 09 2020 02:42:39
%S A321902 1,1,3,1,3,5,7,1,11,5,7,9,3,13,15,1,27,21,23,9,19,29,15,17,11,5,7,25,
%T A321902 3,13,31,1,59,21,55,9,51,29,47,17,43,37,39,25,35,45,31,33,27,53,23,41,
%U A321902 19,61,15,49,11,5,7,57,3,13,63
%N A321902 Irregular table read by rows: T(n,k) = (2*k+1)^(1/(2*k+1)) mod 2^n, 0 <= k <= 2^(n-1) - 1.
%C A321902 T(n,k) is the unique x in {1, 3, 5, ..., 2^n - 1} such that x^(2*k+1) == 2*k + 1 (mod 2^n).
%C A321902 The n-th row contains 2^(n-1) numbers, and is a permutation of the odd numbers below 2^n.
%C A321902 For all n, k we have v(T(n,k)-1, 2) = v(k, 2) + 1 and v(T(n,k)+1, 2) = v(k+1, 2) + 1, where v(k, 2) = A007814(k) is the 2-adic valuation of k.
%C A321902 For n >= 3, T(n,k) = 2*k + 1 iff k is divisible by 2^floor((n-1)/2) or k = 2^(n-2) - 1 or k = 2^(n-1) - 1.
%C A321902 T(n,k) is the multiplicative inverse of A321903(n,k) modulo 2^n.
%F A321902 T(n,k) = 2^n - A321903(n,2^(n-1)-1-k).
%e A321902 Table starts
%e A321902 1,
%e A321902 1, 3,
%e A321902 1, 3, 5, 7,
%e A321902 1, 11, 5, 7, 9, 3, 13, 15,
%e A321902 1, 27, 21, 23, 9, 19, 29, 15, 17, 11, 5, 7, 25, 3, 13, 31,
%e A321902 1, 59, 21, 55, 9, 51, 29, 47, 17, 43, 37, 39, 25, 35, 45, 31, 33, 27, 53, 23, 41, 19, 61, 15, 49, 11, 5, 7, 57, 3, 13, 63,
%e A321902 ...
%o A321902 (PARI) T(n, k) = my(m=1); while(Mod(m, 2^n)^(2*k+1)!=2*k+1, m+=2); m
%o A321902 tabf(nn) = for(n=1, nn, for(k=0, 2^(n-1)-1, print1(T(n, k), ", ")); print)
%Y A321902 Cf. A007814.
%Y A321902 {x^x} and its inverse: A320561 & A320562.
%Y A321902 {x^(-x)} and its inverse: A321901 & A321904.
%Y A321902 {x^(1/x)} and its inverse: this sequence & A321905.
%Y A321902 {x^(-1/x)} and its inverse: A321903 & A321906.
%K A321902 nonn,tabf
%O A321902 1,3
%A A321902 _Jianing Song_, Nov 21 2018