login
A323554
Irregular table read by rows: T(n,k) = (2*k+1)^(-1/5) mod 2^n, 0 <= k <= 2^(n-1) - 1.
5
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, 1, 91, 61, 87, 89, 115, 85, 47, 49, 11, 109, 7, 9, 35, 5, 95, 97, 59, 29, 55, 57, 83, 53, 15, 17, 107, 77, 103, 105, 3, 101, 63
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
Cf. A007814.
{(2*k+1)^e mod 2^n}: A323495 (e=-1), A323553 (e=-1/3), this sequence (e=-1/5), A323555 (e=1/5), A323556 (e=1/3).
Sequence in context: A321902 A321905 A323495 * A323556 A338329 A234587
KEYWORD
nonn,tabf
AUTHOR
Jianing Song, Aug 30 2019
EXTENSIONS
Corrected by Robert Israel, Dec 15 2020
STATUS
approved