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A280015 a(n) is the least k such that A056619(k) = prime(n). 0


%S 1,2,12,10,6,76,114,34,120,246,1386,616,1126,3774,510,8220,2634,25810,

%T 57936,46836,12180,254940,54574,80040,497146,801780,402324,1003744,

%U 6441196,2858890,27821214,14312640,47848164,25049814,8454126,45433894,4262890

%N a(n) is the least k such that A056619(k) = prime(n).

%C a(n) is the least number that is a primitive root mod prime(n) but not mod any lower prime.

%C Using the Chinese Remainder Theorem, it is easy to show that such k always exists.

%e 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.

%p a[1]:= 1: a[2]:= 2: p:= 3:

%p Cands:= {4,seq(seq(6*i+j,j=[0,4]),i=1..10^7)}:

%p for n from 3 while Cands <> {} do

%p p:= nextprime(p);

%p r:= numtheory:-primroot(p);

%p s:= select(t -> igcd(t,p-1)=1, {$1..p-1});

%p q:= map(t -> r &^t mod p, s);

%p R,Cands:= selectremove(t -> member(t mod p, q), Cands):

%p if R = {} then break fi;

%p a[n]:= min(R);

%p od:

%p seq(a[i],i=1..n-1);

%Y Cf. A056619.

%K nonn

%O 1,2

%A _Robert Israel_, Feb 21 2017

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Last modified May 16 17:24 EDT 2022. Contains 353712 sequences. (Running on oeis4.)