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A280015 a(n) is the least k such that A056619(k) = prime(n). 0
1, 2, 12, 10, 6, 76, 114, 34, 120, 246, 1386, 616, 1126, 3774, 510, 8220, 2634, 25810, 57936, 46836, 12180, 254940, 54574, 80040, 497146, 801780, 402324, 1003744, 6441196, 2858890, 27821214, 14312640, 47848164, 25049814, 8454126, 45433894, 4262890 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n) is the least number that is a primitive root mod prime(n) but not mod any lower prime.
Using the Chinese Remainder Theorem, it is easy to show that such k always exists.
LINKS
EXAMPLE
10 is a primitive root mod prime(4) = 7, but not mod 2, 3 or 5. This is the least number with that property, so a(4)=10.
MAPLE
a[1]:= 1: a[2]:= 2: p:= 3:
Cands:= {4, seq(seq(6*i+j, j=[0, 4]), i=1..10^7)}:
for n from 3 while Cands <> {} do
p:= nextprime(p);
r:= numtheory:-primroot(p);
s:= select(t -> igcd(t, p-1)=1, {$1..p-1});
q:= map(t -> r &^t mod p, s);
R, Cands:= selectremove(t -> member(t mod p, q), Cands):
if R = {} then break fi;
a[n]:= min(R);
od:
seq(a[i], i=1..n-1);
CROSSREFS
Cf. A056619.
Sequence in context: A166544 A081468 A216349 * A343645 A245281 A358505
KEYWORD
nonn
AUTHOR
Robert Israel, Feb 21 2017
STATUS
approved

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Last modified March 1 05:26 EST 2024. Contains 370430 sequences. (Running on oeis4.)