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A309680
The smallest nonsquare nonzero integer that is a quadratic residue modulo n, or 0 if no such integer exists.
1
0, 0, 0, 0, 0, 3, 2, 0, 7, 5, 3, 0, 3, 2, 6, 0, 2, 7, 5, 5, 7, 3, 2, 12, 6, 3, 7, 8, 5, 6, 2, 17, 3, 2, 11, 13, 3, 5, 3, 20, 2, 7, 6, 5, 10, 2, 2, 33, 2, 6, 13, 12, 6, 7, 5, 8, 6, 5, 3, 21, 3, 2, 7, 17, 10, 3, 6, 8, 3, 11, 2, 28, 2, 3, 6, 5, 11, 3, 2, 20, 7
OFFSET
1,6
FORMULA
a(n) = 2 for n in A057126 and n > 2. - Michel Marcus, Aug 24 2019
EXAMPLE
For n=5, the nonzero quadratic residues modulo 5 are 1 and 4. Since these are both squares we have a(5) = 0.
For n=6, the nonzero quadratic residues modulo 6 are 1,3, and 4. Since 3 is not a square we have a(6) = 3.
For n=10, the nonzero quadratic residues modulo 10 are 1,4,5,6,9. Since 5 is the least nonsquare value, we have a(10) = 5.
MATHEMATICA
a[n_] := SelectFirst[ Union@ Mod[Range[n-1]^2, n], ! IntegerQ@ Sqrt@ # &, 0]; Array[a, 81] (* Giovanni Resta, Aug 13 2019 *)
PROG
(PARI) a(n) = my(v=select(x->issquare(x), vector(n-1, k, Mod(k, n)), 1), y = select(x->!issquare(x), Vec(v))); if (#y, y[1], 0); \\ Michel Marcus, Aug 16 2019
CROSSREFS
A330404 is an alternate version.
Sequence in context: A080779 A355090 A319830 * A010604 A067585 A173787
KEYWORD
nonn
AUTHOR
John Prosser, Aug 12 2019
STATUS
approved