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A306220
a(n) is the smallest prime p such that Kronecker(-n,p) = -1.
3
3, 5, 2, 3, 2, 13, 3, 5, 7, 3, 2, 5, 2, 11, 7, 3, 5, 5, 2, 11, 2, 3, 5, 13, 3, 11, 2, 3, 2, 7, 3, 5, 5, 3, 2, 7, 2, 5, 7, 3, 13, 5, 2, 7, 2, 3, 5, 5, 3, 7, 2, 3, 2, 13, 3, 11, 5, 3, 2, 7, 2, 5, 5, 3, 7, 19, 2, 5, 2, 3, 7, 5, 3, 7, 2, 3, 2, 5, 3, 11, 7, 3, 2, 13, 2, 7, 5
OFFSET
1,1
COMMENTS
A companion sequence to A092419.
Conjecture: lim sup log(a(n))/log(n) = 0. For example, it seems that log(a(n))/log(n) < 0.5 for all n > 1364.
LINKS
FORMULA
a(n) = 2 if and only if n == 3, 5 (mod 8). See A047621.
a(n) = 3 if and only if n == 1, 4, 7, 10, 16, 22 (mod 24).
MAPLE
# This requires Maple 2016 or later
f:= proc(n) local p;
p:= 2;
while NumberTheory:-KroneckerSymbol(-n, p) <> -1 do p:= nextprime(p) od:
p
end proc:
map(f, [$1..100]); # Robert Israel, Feb 17 2019
MATHEMATICA
a[n_] := For[p = 2, True, p = NextPrime[p], If[KroneckerSymbol[-n, p] == -1, Return[p]]];
Array[a, 100] (* Jean-François Alcover, Jun 18 2020 *)
PROG
(PARI) a(n) = forprime(p=2, , if(kronecker(-n, p)<0, return(p)))
CROSSREFS
Cf. A092419.
See A306224 for another version.
Sequence in context: A091276 A282574 A076562 * A057673 A279398 A241429
KEYWORD
nonn
AUTHOR
Jianing Song, Jan 29 2019
STATUS
approved