

A333669


The smallest square > 1 modulo n.


1



4, 3, 2, 4, 4, 4, 3, 4, 3, 2, 4, 4, 2, 4, 4, 4, 4, 3, 2, 4, 4, 3, 4, 4, 4, 4, 2, 4, 3, 2, 4, 4, 3, 4, 3, 4, 2, 4, 4, 4, 4, 2, 2, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 3, 2, 4, 4, 4, 3, 4, 4, 3, 4, 2, 4, 2, 3, 4, 4, 4, 3, 2, 4, 4, 2, 3, 4, 4, 4, 4, 4
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OFFSET

5,1


COMMENTS

The values are 2, 3 and 4. If 2 is a square modulo n (see A057126) the value is 2. Otherwise, if 3 is a square modulo n (see A057125) the value is 3. If neither 2 or 3 are a square modulo n the value is 4.
Dedicated to Urs Meyer at the occasion of his 60th birthday.


LINKS

Robert Israel, Table of n, a(n) for n = 5..10000


EXAMPLE

The squares modulo 5 are 1 and 4, therefore a(5) = 4. Modulo 6 the squares are 1, 3 and 4 which makes a(6) = 3. a(7) = 2 since 2 = 3^2 modulo 7.


MAPLE

f:= proc(n) uses numtheory; if quadres(2, n)=1 then 2 elif quadres(3, n)=1 then 3 else 4 fi end proc:
map(f, [$5..100]); # Robert Israel, Sep 15 2020


MATHEMATICA

qrQ[m_, n_] := Module[{k}, Reduce[Mod[mk^2, n]==0, k, Integers] =!= False];
a[n_] := If[qrQ[2, n], 2, If[qrQ[3, n], 3, 4]];
a /@ Range[5, 100] (* JeanFrançois Alcover, Oct 25 2020 *)


PROG

(PARI) a(n) = if(issquare(Mod(2, n)), 2, issquare(Mod(3, n)), 3, 4)


CROSSREFS

Cf. A057126 for the n where the value is 2 and A057125 for the n where the value is 3 if n was not in A057126.
Sequence in context: A304240 A244951 A110631 * A159846 A071890 A167837
Adjacent sequences: A333666 A333667 A333668 * A333670 A333671 A333672


KEYWORD

nonn,easy


AUTHOR

Peter Schorn, May 07 2020


STATUS

approved



