A060203 Least cube root of unity mod p, greater than 1, where p is the n-th prime congruent to 1 mod 3.

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, 28, 116, 44, 17, 98, 31, 128, 122, 83, 88, 51, 34, 53, 20, 198, 171, 133, 21, 232, 139, 60, 129, 40, 109, 213, 24, 210, 65, 252, 43, 177, 296, 255, 253, 227, 281, 307, 320, 72

Offset

1,1

Comments

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.

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

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

Prog

(PARI) cbrt1(p) = {for (i=2, p, if (Mod(i, p)^3 == 1, return(i)); ); }
lista(nn) = {forprime(p=1, nn, if ((p%3) == 1, print1(cbrt1(p), ", "); ); ); } \\ Michel Marcus, Jul 17 2020
(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

Crossrefs

Cf. A002476.

Sequence in context: A128804 A223702 A120726 * A131880 A045790 A159842

Adjacent sequences: A060200 A060201 A060202 * A060204 A060205 A060206

Keyword

nonn

Author

Jud McCranie, Mar 18 2001

Extensions

Offset 1 from Bob Selcoe, Jul 17 2020

Name clarified by Michel Marcus, Jul 17 2020

Status

approved