OFFSET
1,3
COMMENTS
T(n,k) is the unique x in {1, 3, 5, ..., 2^n - 1} such that x^5*(2*k+1) == 1 (mod 2^n).
The n-th row contains 2^(n-1) numbers, and is a permutation of the odd numbers below 2^n.
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.
T(n,k) is the multiplicative inverse of A323555(n,k) modulo 2^n.
LINKS
Robert Israel, Table of n, a(n) for n = 1..16383 (rows 1 to 14, flattened)
EXAMPLE
Table starts
1,
1, 3,
1, 3, 5, 7,
1, 11, 13, 7, 9, 3, 5, 15,
1, 27, 29, 23, 25, 19, 21, 15, 17, 11, 13, 7, 9, 3, 5, 31
1, 27, 61, 23, 25, 51, 21, 47, 49, 11, 45, 7, 9, 35, 5, 31, 33, 59, 29, 55, 57, 19, 53, 15, 17, 43, 13, 39, 41, 3, 37, 63
...- corrected by Robert Israel, Dec 15 2020
MAPLE
for n from 1 to 8 do
seq(numtheory:-mroot(2*k+1, -5, 2^n), k=0..2^(n-1)-1)
od; # Robert Israel, Dec 15 2020
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Jianing Song, Aug 30 2019
EXTENSIONS
Corrected by Robert Israel, Dec 15 2020
STATUS
approved