A142457 A triangular sequence "representation" of the modulo 11 Integer field: t(+)(n,m)=Mod[n + m, 11]; t(x)(n,m)=Mod[n*m, 11]; t(n,m)=Mod[t(=)(n,m)*t(X)(n,m),11].

0, 0, 2, 0, 6, 5, 0, 1, 8, 10, 0, 9, 4, 7, 7, 0, 8, 4, 10, 4, 8, 0, 9, 8, 8, 9, 0, 3, 0, 1, 5, 1, 0, 2, 7, 4, 0, 6, 6, 0, 10, 3, 1, 4, 1, 0, 2, 0, 5, 6, 3, 7, 7, 3, 6, 0, 0, 9, 5, 10, 2, 3, 2, 10, 5, 9

Offset

1,3

Comments

Row sums are:

{0, 2, 11, 19, 27, 34, 37, 20, 31, 39, 55}.

Modulo eleven they are:

{0, 2, 0, 8, 5, 1, 4, 9, 9, 6, 0}.

The representation is "faithful": all the digits show up.

In "Infinity" is like "odd" : even*odd=odd

1/Infinity=0

then

Mod[n+m,Infinity]

Mod[n*m,Infinity]

Representation of Integer field"Z"=Mod[Mod[n+m,Infinity]*Mod[n*m,Infinity],Infinity]

is like 11 not 10?

The primes as the Algebraic geometry people seem to think?

Links

Table of n, a(n) for n=1..66.

Formula

t(+)(n,m)=Mod[n + m, 11]; t(x)(n,m)=Mod[n*m, 11]; t(n,m)=Mod[t(=)(n,m)*t(X)(n,m),11].

Example

{0},
{0, 2},
{0, 6, 5},
{0, 1, 8, 10},
{0, 9, 4, 7, 7},
{0, 8, 4, 10, 4, 8},
{0, 9, 8, 8, 9, 0, 3},
{0, 1, 5, 1, 0, 2, 7, 4},
{0, 6, 6, 0, 10, 3, 1, 4, 1},
{0, 2, 0, 5, 6, 3, 7, 7, 3, 6},
{0, 0, 9, 5, 10, 2, 3, 2, 10, 5, 9}

Mathematica

Clear[t1, t2, t, n, m, a] t1[n_, m_] = Mod[n + m, 11] t2[n_, m_] = Mod[n*m, 11] t[n_, m_] = Mod[t1[n, m]*t2[n, m], 11] a = Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A335728 A078037 A088508 * A100711 A199464 A189961

Adjacent sequences: A142454 A142455 A142456 * A142458 A142459 A142460

Keyword

nonn,uned

Author

Roger L. Bagula and Gary W. Adamson, Sep 19 2008

Status

approved