A141658 A triangle of coefficients representing an Integer Irrational rotation of the primes: t(n,m)=Floor[Re[Exp[I*2*Pi*Mod[m*2*Pi, 1]/(n + 2)]*Prime[n + 1]]]. ( Correction with right numbers).

2, 3, 2, 5, 4, 3, 7, 6, 5, 3, 11, 10, 9, 6, 10, 13, 12, 11, 9, 12, 12, 17, 16, 15, 13, 16, 16, 14, 19, 18, 17, 15, 18, 18, 16, 14, 23, 22, 21, 19, 22, 22, 20, 18, 22, 29, 28, 27, 25, 28, 28, 26, 24, 28, 27, 31, 30, 29, 27, 30, 30, 28, 26, 30, 29, 28

Offset

1,1

Comments

Row sums are:

{2, 5, 12, 21, 46, 69, 107, 135, 189, 270, 318}.

Links

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

Formula

t(n,m)=Floor[Re[Exp[I*2*Pi*Mod[m*2*Pi, 1]/(n + 2)]*Prime[n + 1]]].

Example

{2},
{3, 2},
{5, 4, 3},
{7, 6, 5, 3},
{11, 10, 9, 6, 10},
{13, 12, 11, 9, 12, 12},
{17, 16, 15, 13, 16, 16, 14},
{19, 18, 17, 15, 18, 18, 16, 14},
{23, 22, 21, 19, 22, 22, 20, 18, 22},
{29, 28, 27, 25, 28, 28, 26, 24, 28, 27},
{31, 30, 29, 27, 30, 30, 28, 26, 30, 29, 28}

Mathematica

Clear[T, n, m]; T[n_, m_] = Floor[Cyclotomic[Prime[n + 1], m/(n + 2)]*Prime[n + 1]]; Table[Flatten[Table[If[PrimeQ[T[n, m]], T[n, m], {}], {m, 0, n}]], {n, 0, 10}]; Flatten[%]

Crossrefs

Cf. A141529.

Sequence in context: A197702 A075861 A205706 * A350169 A089587 A278327

Adjacent sequences: A141655 A141656 A141657 * A141659 A141660 A141661

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Sep 04 2008

Status

approved