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A063988
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Triangle in which n-th row gives quadratic non-residues modulo the n-th prime.
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2
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2, 2, 3, 3, 5, 6, 2, 6, 7, 8, 10, 2, 5, 6, 7, 8, 11, 3, 5, 6, 7, 10, 11, 12, 14, 2, 3, 8, 10, 12, 13, 14, 15, 18, 5, 7, 10, 11, 14, 15, 17, 19, 20, 21, 22, 2, 3, 8, 10, 11, 12, 14, 15, 17, 18, 19, 21, 26, 27, 3, 6, 11, 12, 13, 15, 17, 21, 22, 23, 24, 26, 27, 29, 30, 2, 5, 6, 8, 13, 14
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OFFSET
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2,1
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LINKS
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EXAMPLE
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Mod the 5th prime, 11, the quadratic residues are 1,3,4,5,9 and the non-residues are 2,6,7,8,10.
Triangle begins:
2;
2,3;
3,5,6;
2,6,7,8,10;
...
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MAPLE
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with(numtheory): for n from 1 to 20 do for j from 1 to ithprime(n)-1 do if legendre(j, ithprime(n)) = -1 then printf(`%d, `, j) fi; od: od:
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MATHEMATICA
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row[n_] := Select[p = Prime[n]; Range[p - 1], JacobiSymbol[#, p] == -1 &]; Table[row[n], {n, 2, 12}] // Flatten (* Jean-François Alcover, Oct 17 2012 *)
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PROG
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(PARI) residue(n, m)={local(r); r=0; for(i=0, floor(m/2), if(i^2%m==n, r=1)); r}
(PARI) tabf(nn) = {for(n=1, prime(nn), p = prime(n); for (i=2, p-1, if (kronecker(i, p) == -1, print1(i, ", ")); ); print(); ); } \\ Michel Marcus, Jul 19 2013
(Python)
from sympy import jacobi_symbol as J, prime
def a(n):
p=prime(n)
return [i for i in range(1, p) if J(i, p)==-1]
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CROSSREFS
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KEYWORD
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nonn,tabf,nice,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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