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A157415
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Triangle t(n,m) = Jacobi(prime(n) / prime(m)) + Jacobi( prime(n)/ prime(n-m+2)), 2<=m<=n.
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1
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 2,5
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COMMENTS
| Row sums are 0, -2, 0, 2, -4, -6, 0, 2, 0, -2,...
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FORMULA
| t(n,m) = A157412(n,m)+A157412(n,n-m+2). - R. J. Mathar, Sep 12 2011
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EXAMPLE
| 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;
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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
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MATHEMATICA
| Table[Table[JacobiSymbol[Prime[n], Prime[m]] + JacobiSymbol[Prime[n], Prime[n - m + 2]], {m, 2, n}], {n, 2, 11}];
Flatten[%]
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CROSSREFS
| Sequence in context: A023589 A134034 A174886 * A154325 A129765 A143187
Adjacent sequences: A157412 A157413 A157414 * A157416 A157417 A157418
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KEYWORD
| sign,tabl
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 28 2009
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