login
A157415
Triangle read by rows: T(n,m) = Jacobi(prime(n)/prime(m)) + Jacobi(prime(n)/prime(n-m+2)), 2 <= m <= n.
1
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, ...
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
KEYWORD
sign,tabl,less
AUTHOR
Roger L. Bagula, Feb 28 2009
STATUS
approved