A157415 Triangle read by rows: T(n,m) = Jacobi(prime(n)/prime(m)) + Jacobi(prime(n)/prime(n-m+2)), 2 <= m <= n.

0, -1, -1, 1, -2, 1, -1, 2, 2, -1, 1, -2, -2, -2, 1, -1, 0, -2, -2, 0, -1, 1, 2, -2, -2, -2, 2, 1, -1, 0, 0, 2, 2, 0, 0, -1, -1, 2, 0, -2, 2, -2, 0, 2, -1, 1, 0, 0, 0, -2, -2, 0, 0, 0, 1

Offset

2,5

Comments

Row sums are 0, -2, 0, 2, -4, -6, 0, 2, 0, -2, ...

Links

Table of n, a(n) for n=2..56.

Formula

T(n,m) = A157412(n,m) + A157412(n,n-m+2). - R. J. Mathar, Sep 12 2011

Example

Triangle begins
   0;
  -1, -1;
   1, -2,  1;
  -1,  2,  2, -1;
   1, -2, -2, -2,  1;
  -1,  0, -2, -2,  0, -1;
   1,  2, -2, -2, -2,  2,  1;
  -1,  0,  0,  2,  2,  0,  0, -1;
  -1,  2,  0, -2,  2, -2,  0,  2, -1;
   1,  0,  0,  0, -2, -2,  0,  0,  0,  1;

Maple

A157412 := proc(n, m)
        numtheory[jacobi](ithprime(n), ithprime(m
end proc:
A157415 := proc(n, m)
        A157412(n, m)+A157412(n, n-m+2) ;
end proc:
seq(seq(A157415(n, m), m=2..n), n=2..13) ; # R. J. Mathar, Sep 12 2011

Mathematica

Table[Table[JacobiSymbol[Prime[n], Prime[m]] + JacobiSymbol[Prime[n], Prime[n - m + 2]], {m, 2, n}], {n, 2, 11}];
Flatten[%]

Crossrefs

Sequence in context: A023589 A134034 A174886 * A154325 A129765 A143187

Adjacent sequences: A157412 A157413 A157414 * A157416 A157417 A157418

Keyword

sign,tabl,less

Author

Roger L. Bagula, Feb 28 2009

Status

approved