

A063988


Triangle in which nth row gives quadratic nonresidues modulo the nth prime.


2



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

2,1


LINKS

T. D. Noe, Rows n=2..100 of triangle, flattened


EXAMPLE

Mod the 5th prime, 11, the quadratic residues are 1,3,4,5,9 and the nonresidues are 2,6,7,8,10.
2; 2,3; 3,5,6; 2,6,7,8,10; ...


MAPLE

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:


MATHEMATICA

row[n_] := Select[p = Prime[n]; Range[p  1], JacobiSymbol[#, p] == 1 &]; Table[row[n], {n, 2, 12}] // Flatten (* JeanFrançois Alcover, Oct 17 2012 *)


PROG

(PARI) residue(n, m)={local(r); r=0; for(i=0, floor(m/2), if(i^2%m==n, r=1)); r}
isA063988(n, m)=!residue(n, prime(m)) \\ Michael B. Porter, May 07 2010
(PARI) tabf(nn) = {for(n=1, prime(nn), p = prime(n); for (i=2, p1, 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 list(filter(lambda i: J(i, p)==1, range(1, p)))
for n in xrange(2, 13): print a(n) # Indranil Ghosh, May 27 2017


CROSSREFS

Cf. A063987.
Sequence in context: A166588 A277321 A262365 * A198453 A178932 A206439
Adjacent sequences: A063985 A063986 A063987 * A063989 A063990 A063991


KEYWORD

nonn,tabf,nice,easy


AUTHOR

Suggested by Gary W. Adamson, Sep 18 2001


EXTENSIONS

More terms from James A. Sellers, Sep 25 2001


STATUS

approved



