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 A063988 Triangle in which n-th row gives quadratic non-residues modulo the n-th prime. 2

%I

%S 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,

%T 13,14,15,18,5,7,10,11,14,15,17,19,20,21,22,2,3,8,10,11,12,14,15,17,

%U 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

%N Triangle in which n-th row gives quadratic non-residues modulo the n-th prime.

%H T. D. Noe, <a href="/A063988/b063988.txt">Rows n=2..100 of triangle, flattened</a>

%e Mod the 5-th prime, 11, the quadratic rseidues are 1,3,4,5,9 and the non-residues are 2,6,7,8,10.

%e 2; 2,3; 3,5,6; 2,6,7,8,10; ...

%p 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:

%t 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 *)

%o Contribution from _Michael B. Porter_, May 07 2010: (Start)

%o (PARI) residue(n,m)={local(r);r=0;for(i=0,floor(m/2),if(i^2%m==n,r=1));r}

%o isA063988(n,m)=!residue(n,prime(m)) (End)

%Y Cf. A063987.

%K nonn,tabf,nice,easy

%O 2,1

%A Suggested by Gary W. Adamson, Sep 18 2001

%E More terms from _James A. Sellers_, Sep 25 2001

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