A142354 A triangular sequence "representation" of the modulo 10 Integer field: t(+)(n,m)=Mod[n + m, 10]; t(x)(n,m)=Mod[n*m, 10]; t(n,m)=Mod[t(=)(n,m)*t(X)(n,m),10].

0, 0, 2, 0, 6, 6, 0, 2, 0, 4, 0, 0, 8, 4, 8, 0, 0, 0, 0, 0, 0, 0, 2, 6, 2, 0, 0, 2, 0, 6, 6, 0, 8, 0, 6, 6, 0, 2, 0, 4, 4, 0, 2, 0, 4, 0, 0, 8, 4, 8, 0, 0, 8, 4, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,3

Comments

Row sums are:

{0, 2, 12, 6, 20, 0, 12, 32, 16, 40, 0}.

Modulo ten they are:

{0, 2, 2, 6, 0, 0, 2, 2, 6, 0, 0}.

The block:

{0},

{0, 2},

{0, 6, 6},

{0, 2, 0, 4},

{0, 0, 8, 4, 8},

{0, 0, 0, 0, 0, 0},

shows up in three places.

Only even {0,2,4,6,8} show up.

It may be a field representation, but can you get the

original tables back from it?

Links

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

Formula

t(+)(n,m)=Mod[n + m, 10]; t(x)(n,m)=Mod[n*m, 10]; t(n,m)=Mod[t(=)(n,m)*t(X)(n,m),10].

Example

{0},
{0, 2},
{0, 6, 6},
{0, 2, 0, 4},
{0, 0, 8, 4, 8},
{0, 0, 0, 0, 0, 0},
{0, 2, 6, 2, 0, 0, 2},
{0, 6, 6, 0, 8, 0, 6, 6},
{0, 2, 0, 4, 4, 0, 2, 0, 4},
{0, 0, 8, 4, 8, 0, 0, 8, 4, 8},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

Mathematica

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

Crossrefs

Sequence in context: A145419 A276763 A338465 * A105110 A351884 A342501

Adjacent sequences: A142351 A142352 A142353 * A142355 A142356 A142357

Keyword

nonn,uned

Author

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

Status

approved