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Least cube root of unity mod p, greater than 1, where p is the n-th prime congruent to 1 mod 3.
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%I #17 Jul 17 2020 10:52:04

%S 2,3,7,5,10,6,13,29,8,23,35,46,45,19,42,32,12,58,48,84,92,14,39,94,15,

%T 28,116,44,17,98,31,128,122,83,88,51,34,53,20,198,171,133,21,232,139,

%U 60,129,40,109,213,24,210,65,252,43,177,296,255,253,227,281,307,320,72

%N Least cube root of unity mod p, greater than 1, where p is the n-th prime congruent to 1 mod 3.

%C The cube roots of unity mod p, the n-th prime congruent to 1 mod 3 (A002476), are 1, a(n) and p-a(n)-1.

%C That is, the smaller root of x^2 + x + 1 (mod p) where p is the n-th prime = 1 mod 3. - _Charles R Greathouse IV_, Jul 17 2020

%H Charles R Greathouse IV, <a href="/A060203/b060203.txt">Table of n, a(n) for n = 1..10000</a>

%e The 5th prime == 1 (mod 3) is 37, 10^3 == 1 (mod 37), so a(5)=10.

%o (PARI) cbrt1(p) = {for (i=2, p, if (Mod(i,p)^3 == 1, return(i)););}

%o lista(nn) = {forprime(p=1, nn, if ((p%3) == 1, print1(cbrt1(p), ", ");););} \\ _Michel Marcus_, Jul 17 2020

%o (PARI) do(x)=my(P=select(p->p%3==1, primes([2,x])),v); v=apply(p->lift((sqrt(Mod(-3,p))-1)/2), P); vector(#P,i, min(v[i], P[i]-v[i]-1)) \\ _Charles R Greathouse IV_, Jul 17 2020

%Y Cf. A002476.

%K nonn

%O 1,1

%A _Jud McCranie_, Mar 18 2001

%E Offset 1 from _Bob Selcoe_, Jul 17 2020

%E Name clarified by _Michel Marcus_, Jul 17 2020