A105878 -id:A105878 - cp's OEIS frontend

A167802 Numbers with primitive root -6.

13, 17, 19, 23, 41, 47, 61, 67, 71, 89, 109, 113, 137, 157, 167, 169, 211, 229, 233, 257, 263, 277, 283, 289, 331, 359, 361, 373, 383, 397, 401, 449, 479, 503, 521, 523, 529, 547, 569, 593, 599, 613, 619, 641, 647, 661, 691, 709, 719, 733, 739, 743, 757, 761

Offset: 1

T. D. Noe, Nov 12 2009

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A105878 (primes with primitive root -6)

pr=-6; Select[Range[2,2000], MultiplicativeOrder[pr,# ] == EulerPhi[ # ] &]

is(n)=gcd(n,6)==1 && znorder(Mod(-6,n))==eulerphi(n) && n>1 \\ Charles R Greathouse IV, Feb 23 2017

A380533 a(n) is the multiplicative order of -6 modulo prime(n); a(1) = a(2) = 0 for completion.

Original entry on oeis.org

0, 0, 2, 1, 5, 12, 16, 18, 22, 7, 3, 4, 40, 6, 46, 13, 29, 60, 66, 70, 36, 39, 41, 88, 12, 5, 51, 53, 108, 112, 63, 65, 136, 46, 74, 75, 156, 54, 166, 86, 89, 60, 38, 96, 7, 99, 210, 111, 113, 228, 232, 34, 20, 125, 256, 262, 67, 135, 276, 56

Offset: 1

Jianing Song, Jun 27 2025

Jianing Song, Table of n, a(n) for n = 1..10000

Cf. A105878 (primes having primitive root -6).
Cf. bases 2..10: A014664, A062117, A082654, A211241, A211242, A211243, A211244, A211245, A002371.
Cf. bases -2..-10: A337878 (if first term 1), A380482, A380531, A380532, this sequence, A380540, A380541, A380542, A385222.

A380533[n_] := If[n < 3, 0, MultiplicativeOrder[-6, Prime[n]]];
Array[A380533, 100] (* Paolo Xausa, Jun 29 2025 *)

a(n,{k=-6}) = my(p = prime(n)); if(k%p==0, 0, znorder(Mod(k,p)))

cp's OEIS Frontend

A167802 Numbers with primitive root -6.

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