A038882 -id:A038882 - cp's OEIS frontend

A019339 Primes with primitive root 11.

2, 3, 13, 17, 23, 29, 31, 41, 47, 59, 67, 71, 73, 101, 103, 109, 149, 163, 173, 179, 197, 223, 233, 251, 277, 281, 293, 331, 367, 373, 383, 419, 443, 461, 463, 467, 487, 499, 557, 569, 587, 593, 599, 601, 613, 619, 643, 647, 673, 677, 683, 701, 719, 761, 769, 809, 821

Offset: 1

David W. Wilson

nonn

To allow primes less than the specified primitive root m (here, 11) to be included, we use the essentially equivalent definition "Primes p such that the multiplicative order of m mod p is p-1". This comment applies to all of A019334-A019421. - N. J. A. Sloane, Dec 03 2019

This is a subsequence of A038882. - Klaus Purath, Jul 03 2023

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for primes by primitive root

Cf. A071566.

pr=11; Select[Prime[Range[200]], MultiplicativeOrder[pr, # ] == #-1 &]

A296936 Inert rational primes in the field Q(sqrt(11)).

Original entry on oeis.org

3, 13, 17, 23, 29, 31, 41, 47, 59, 61, 67, 71, 73, 101, 103, 109, 149, 163, 173, 179, 191, 193, 197, 199, 223, 233, 241, 251, 277, 281, 293, 311, 331, 337, 349, 367, 373, 379, 383, 409, 419, 443, 457, 461, 463, 467, 487, 499, 541, 557, 569, 587, 593, 599, 601

Offset: 1

N. J. A. Sloane, Dec 26 2017

Cf. A296935, A038881, A038882.

Load the Maple program HH given in A296920. Then run HH(11, 200); This produces A296935, A296936, A038881, A038882.

Select[Prime[Range[2, 120]], KroneckerSymbol[11, #] == -1 &] (* Amiram Eldar, Dec 24 2023 *)

A038881 Odd primes p such that 11 is a square mod p.

Original entry on oeis.org

5, 7, 11, 19, 37, 43, 53, 79, 83, 89, 97, 107, 113, 127, 131, 137, 139, 151, 157, 167, 181, 211, 227, 229, 239, 257, 263, 269, 271, 283, 307, 313, 317, 347, 353, 359, 389, 397, 401, 421, 431, 433, 439, 449, 479, 491, 503, 509, 521, 523, 547, 563, 571, 577

Offset: 1

N. J. A. Sloane

Also, only entries p=1 (mod 4) of the sequence are squares mod 11 (from the quadratic reciprocity law). - Lekraj Beedassy, Jul 21 2004

Zak Seidov, Table of n, a(n) for n = 1..10000

Cf. A038882.

[p: p in PrimesInInterval(3,577) | not JacobiSymbol(11,p) eq -1]; // Bruno Berselli, Sep 10 2012

Select[Prime[Range[120]],! JacobiSymbol[11, #]== -1 &] (* Vincenzo Librandi, Sep 10 2012 *)

forprime(p=2,1000,if(kronecker(11,p)==+1,print1(p,", "))) /* Joerg Arndt, Apr 24 2011 */

Added "odd" to definition (otherwise 2 would be a term). - N. J. A. Sloane, Jul 04 2023

A296935 Rational primes that decompose in the field Q(sqrt(11)).

Original entry on oeis.org

5, 7, 19, 37, 43, 53, 79, 83, 89, 97, 107, 113, 127, 131, 137, 139, 151, 157, 167, 181, 211, 227, 229, 239, 257, 263, 269, 271, 283, 307, 313, 317, 347, 353, 359, 389, 397, 401, 421, 431, 433, 439, 449, 479, 491, 503, 509, 521, 523, 547, 563, 571, 577, 607

Offset: 1

N. J. A. Sloane, Dec 26 2017

Cf. A296936, A038881, A038882.

Load the Maple program HH given in A296920. Then run HH(11, 200); This produces A296935, A296936, A038881, A038882.

Select[Prime[Range[120]], KroneckerSymbol[11, #] == 1 &] (* Amiram Eldar, Dec 24 2023 *)

list(lim)=my(v=List()); forprime(p=5,lim, if(kronecker(11,p)==1, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Mar 18 2018

cp's OEIS Frontend

A019339 Primes with primitive root 11.

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A296936 Inert rational primes in the field Q(sqrt(11)).

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A038881 Odd primes p such that 11 is a square mod p.

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A296935 Rational primes that decompose in the field Q(sqrt(11)).

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Maple

Mathematica

PARI