A320602 -id:A320602 - cp's OEIS frontend

A320561 Irregular table read by rows: T(n,k) = (2k+1)^(2k+1) mod 2^n, 0 <= k <= 2^(n-1) - 1.

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, 3, 13, 31, 1, 27, 53, 55, 9, 19, 61, 47, 17, 11, 5, 39, 25, 3, 13, 31, 33, 59, 21, 23, 41, 51, 29, 15, 49, 43, 37, 7, 57, 35, 45, 63

Offset: 1

Jianing Song, Oct 15 2018

The sequence {k^k mod 2^n} has period 2^n. The n-th row contains 2^(n-1) numbers, and is a permutation of the odd numbers below 2^n.
Note that the first 5 rows are the same as those in A320562, but after that they differ.
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. [Revised by Jianing Song, Nov 24 2018]
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.
T(n,k) is the multiplicative inverse of A321901(n,k) modulo 2^n. - Jianing Song, Nov 24 2018

			Table starts
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, 3, 13, 31,
1, 27, 53, 55, 9, 19, 61, 47, 17, 11, 5, 39, 25, 3, 13, 31, 33, 59, 21, 23, 41, 51, 29, 15, 49, 43, 37, 7, 57, 35, 45, 63,
...

Muniru A Asiru, Table of n, a(n) for n = 1..8191 (Rows n=1..13)

Cf. A007814.
{x^x} and its inverse: this sequence & A320562.
{x^(-x)} and its inverse: A321901 & A321904.
{x^(1/x)} and its inverse: A321902 & A321905.
{x^(-1/x)} and its inverse: A321903 & A321906.

T:= Flat(List([1..6],n->List([0..2^(n-1)-1],k->PowerMod(2*k+1,2*k+1,2^n)))); # Muniru A Asiru, Oct 23 2018

Table[PowerMod[(2 k + 1), (2 k + 1), 2^n], {n, 6}, {k, 0, 2^(n - 1) - 1}] // Flatten (* Michael De Vlieger, Oct 22 2018 *)

T(n,k) = lift(Mod(2*k+1, 2^n)^(2*k+1))
tabf(nn) = for(n=1, nn, for(k=0, 2^(n-1)-1, print1(T(n, k), ", ")); print);

T(n,k) = A320602(2^n, 2*k+1).

T(n,k) = 2^n - A321901(n,2^(n-1)-1-k). - Jianing Song, Nov 24 2018

cp's OEIS Frontend

A320561 Irregular table read by rows: T(n,k) = (2k+1)^(2k+1) mod 2^n, 0 <= k <= 2^(n-1) - 1.

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cp's OEIS Frontend

A320561 Irregular table read by rows: T(n,k) = (2*k+1)^(2*k+1) mod 2^n, 0 <= k <= 2^(n-1) - 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

GAP

Mathematica

PARI

Formula

A320561 Irregular table read by rows: T(n,k) = (2k+1)^(2k+1) mod 2^n, 0 <= k <= 2^(n-1) - 1.