A140653 A triangular sequence of cyclotomic polynomial doubling: For cyclotomic polynomial:c(x,n) p(x,n)=c(x,Prime[n])*c(x,2*Prime[n]).

1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0

Offset

1,1

Comments

Row sums are primes except for n=1:

{4, 3, 5, 7, 11, 13, 17, 19, 23, 29}

Links

Table of n, a(n) for n=1..105.

Formula

For cyclotomic polynomial:c(x,n) p(x,n)=c(x,Prime[n])*c(x,2*Prime[n])

Example

{1, 1, 1, 1},
{1, 0, 1, 0, 1},
{1, 0, 1, 0, 1, 0, 1, 0, 1},
{1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1},
{1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1},
{1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1},
{1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1},
{1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1},
{1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1},
{1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1}

Mathematica

Clear[p, x, n] p[x_, n_] = Cyclotomic[Prime[n], x]*Cyclotomic[2*Prime[n], x]; Table[ExpandAll[p[x, n]], {n, 1, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 1, 10}]

Crossrefs

Sequence in context: A333248 A114592 A344864 * A342892 A071036 A071038

Adjacent sequences: A140650 A140651 A140652 * A140654 A140655 A140656

Keyword

nonn,tabf,uned

Author

Roger L. Bagula and Gary W. Adamson, Jul 09 2008

Status

approved