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

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

Offset: 1

Author

Robert Israel, Feb 21 2017

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A056619.

Programs

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);