A003572 -id:A003572 - cp's OEIS frontend

A003574 Order of 4 mod 4n-1.

1, 3, 5, 2, 9, 11, 9, 5, 6, 6, 7, 23, 4, 10, 29, 3, 33, 35, 10, 39, 41, 14, 6, 18, 15, 51, 53, 18, 22, 12, 10, 7, 65, 18, 69, 30, 21, 15, 10, 26, 81, 83, 9, 30, 89, 30, 20, 95, 6, 99, 42, 33, 105, 14, 9, 37, 113, 15, 46, 119

Offset: 1

N. J. A. Sloane

nonn

Muniru A Asiru, Table of n, a(n) for n = 1..10000

Cf. A003573. Second bisection of A053447.

Cf. A002326, A003572, A217852.

List([1..70],n->OrderMod(4,4*n-1)); # Muniru A Asiru, Feb 19 2019

with(numtheory): f := n->order(4,4*n-1);

a(n) = znorder(Mod(4, 4*n-1)); \\ Michel Marcus, Feb 22 2019

a(n) = A053447(2*n-1) for n >= 1. - Jianing Song, Oct 03 2022

A217852 Multiplicative order of 5 (mod 5*n - 1).

Original entry on oeis.org

1, 6, 6, 9, 2, 14, 16, 4, 5, 42, 18, 29, 16, 22, 36, 39, 6, 44, 46, 30, 4, 27, 18, 48, 3, 42, 22, 69, 12, 37, 30, 52, 20, 52, 14, 89, 22, 18, 96, 33, 16, 45, 106, 72, 24, 114, 12, 119, 30, 82, 42, 36, 10, 67, 136, 6, 5, 272, 42, 44, 36, 102, 156, 70, 54, 138, 166

Offset: 1

Arkadiusz Wesolowski, Nov 16 2012

nonn

Least m such that 5*n - 1 divides 5^m - 1.

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Multiplicative Order

Cf. A002326, A003572, A003574, A128858.

List([1..70],n->OrderMod(5,5*n-1)); # Muniru A Asiru, Feb 25 2019

Table[MultiplicativeOrder[5, 5*n - 1], {n, 67}]

vector(80, n, znorder(Mod(5, 5*n-1))) \\ Michel Marcus, Feb 09 2015

A119980 Order of the following permutation on 3n+1 symbols. Write the 3n+1 symbols horizontally into a 3-column grid and read them off vertically, i.e., column after column.

Original entry on oeis.org

1, 3, 6, 6, 11, 15, 52, 38, 51, 9, 360, 260, 35, 39, 364, 1932, 680, 532, 1122, 260, 2415, 3570, 168, 360, 71, 12285, 836, 12, 1680, 1155, 858, 936, 7956, 48300, 171120, 234, 4428, 235752, 712, 990, 119, 364182, 406, 11220, 412920, 25584, 476, 19998, 6486

Offset: 0

Roland Miyamoto, Aug 03 2006

nonn

			For n=2, the grid with 0..6 by rows is
   0 1 2
   3 4 5      first column is one longer
   6
Reading them by columns gives (0,3,6,1,4,2,5) which as a permutation has order 6, so a(2) = 6.

Andrew Howroyd, Table of n, a(n) for n = 0..1000

The case for 2 columns is A002326.

Cf. A003572.

# GAP / KANT / KASH
# SpartaEncrypt(d,L) returns the list M obtained by writing L in d columns
# and then concatenating these columns
SpartaEncrypt := function(d,L)
local len, i, M;
len := Length(L);
M := [];
for i in [1..d] do
Append(M,L{[i,d+i..d*IntQuo(len-i,d)+i]});
od;
return M;
end;
# SpartaOrd(d,m) computes the order of SpartEncrypt(d,[0..m-1])
# in the group S_m
SpartaOrd := function(d,m)
local L, M, i;
M := [0..m-1];
L := [0..m-1];
i := 0;
repeat
i := i + 1;
L := SpartaEncrypt(d,L);
until L=M;
return i;
end;
d:=3; r:=1;
a := List([0..60],n->SpartaOrd(d,d*n+r));

P(n,w,j)={my(c=j%w); if(c==0, j/w, j\w + c*n + 1)}
Follow(s,f)={my(t=f(s), k=1); while(t>s, k++; t=f(t)); if(s==t, k, 0)}
CyclePoly(n,w,x)={my(q=0); for(i=0, w*n, my(l=Follow(i, j->P(n,w,j))); if(l, q+=x^l)); q}
a(n)={my(q=CyclePoly(n, 3, x), m=1); for(i=1, poldegree(q), if(polcoef(q, i), m=lcm(m, i))); m} \\ Andrew Howroyd, Jan 04 2024

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A003574 Order of 4 mod 4n-1.

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A217852 Multiplicative order of 5 (mod 5*n - 1).

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A119980 Order of the following permutation on 3n+1 symbols. Write the 3n+1 symbols horizontally into a 3-column grid and read them off vertically, i.e., column after column.

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