cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A167806 Numbers with primitive root -10.

Original entry on oeis.org

3, 17, 29, 31, 43, 61, 67, 71, 83, 97, 107, 109, 113, 149, 151, 163, 181, 191, 193, 199, 227, 229, 233, 257, 269, 283, 289, 307, 311, 313, 337, 347, 359, 389, 431, 433, 439, 443, 461, 467, 479, 509, 523, 541, 563, 577, 587, 593, 599, 631, 683, 701, 709, 719
Offset: 1

Views

Author

T. D. Noe, Nov 12 2009

Keywords

Comments

Note that the term 289 is not a prime and therefore does not appear in A007348. - Robert G. Wilson v, Aug 18 2014

Links

Crossrefs

Cf. A007348 (primes with primitive root -10).

Programs

  • Mathematica
    pr=-10; Select[Range[2,2000], MultiplicativeOrder[pr,# ] == EulerPhi[ # ] &]
  • PARI
    is(n)=if(gcd(n,10)>1, return(0)); my(p=eulerphi(n)); znorder(Mod(-10,n),p)==p \\ Charles R Greathouse IV, Nov 25 2014

A385222 a(n) is the multiplicative order of -10 modulo prime(n); a(1) = a(3) = 0 for completion.

Original entry on oeis.org

0, 2, 0, 3, 1, 3, 16, 9, 11, 28, 30, 6, 10, 42, 23, 26, 29, 60, 66, 70, 8, 26, 82, 44, 96, 4, 17, 106, 108, 112, 21, 65, 8, 23, 148, 150, 39, 162, 83, 86, 89, 180, 190, 192, 49, 198, 15, 111, 226, 228, 232, 14, 15, 25, 256, 131, 268, 10, 138, 28
Offset: 1

Views

Author

Jianing Song, Jun 27 2025

Keywords

Links

Crossrefs

Cf. A007348 (primes having primitive root -10).
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, A380533, A380540, A380541, A380542, this sequence.

Programs

  • Mathematica
    A385222[n_] := If[n == 1 || n == 3, 0, MultiplicativeOrder[-10, Prime[n]]];
Array[A385222, 100] (* Paolo Xausa, Jun 29 2025 *)
  • PARI
    a(n,{k=-10}) = my(p = prime(n)); if(k%p==0, 0, znorder(Mod(k,p)))

A038880 Primes p such that 10 is not a square mod p.

Original entry on oeis.org

7, 11, 17, 19, 23, 29, 47, 59, 61, 73, 97, 101, 103, 109, 113, 127, 131, 137, 139, 149, 167, 179, 181, 193, 211, 223, 229, 233, 251, 257, 263, 269, 313, 331, 337, 349, 353, 367, 379, 383, 389, 419, 421, 433, 457, 461, 463, 487, 491, 499, 503, 509, 541, 571
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Inert rational primes in the field Q(sqrt(10)). - N. J. A. Sloane, Dec 26 2017
Also primes p such that p divides 5^(p-1)/2 + 2^(p-1)/2. - Cino Hilliard, Sep 06 2004
All primes p such that (p^2 - 1)/24 mod 10 = {2,5}. - Richard R. Forberg, Aug 31 2013
Primes that are 7, 11, 17, 19, 21, 23, 29, or 33 mod 40. - Charles R Greathouse IV, Mar 18 2018
Primes p such that p-1 divided by the number of the digits of the period of 1/p results in an odd number. - Davide Rotondo, Apr 28 2024

Links

Crossrefs

Cf. A007348.

Programs

  • Mathematica
    Select[ Prime@Range[2, 105], JacobiSymbol[10, # ] == -1 &] (* Robert G. Wilson v, Dec 15 2005 *)
  • PARI
    list(lim)=my(v=List()); forprime(p=7,lim, if(kronecker(10,p)<0, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Mar 18 2018
  • Python
    from sympy import isprime, jacobi_symbol
def ok(n): return n%2 == 1 and isprime(n) and jacobi_symbol(10, n) == -1
print([k for k in range(575) if ok(k)]) # Michael S. Branicky, May 24 2022

Formula

a(n) ~ 2n log n. - Charles R Greathouse IV, Mar 18 2018

Extensions

More terms from Robert G. Wilson v, Dec 15 2005

A381590 Primes with primitive root -100.

Original entry on oeis.org

3, 7, 19, 23, 31, 43, 47, 59, 67, 71, 83, 107, 131, 151, 163, 167, 179, 191, 199, 223, 227, 263, 283, 307, 311, 347, 359, 367, 379, 383, 419, 431, 439, 443, 467, 479, 487, 491, 499, 503, 523, 563, 571, 587, 599, 619, 631, 647, 659, 683, 719, 727, 743, 787, 811
Offset: 1

Views

Author

Davide Rotondo, Feb 28 2025

Keywords

Comments

Union of long period primes (A006883) of the form 4k-1 and half period primes (A097443) of the form 4k-1.
Complement of A007349 in the union of A007348 and A001913. - Davide Rotondo, May 23 2025

Crossrefs

Cf. A006883, A097443, A007349, A007348, A001913.

Programs

  • Mathematica
    Select[Prime[Range[150]], MultiplicativeOrder[-100, #] == # - 1 &]  (* Amiram Eldar, Mar 02 2025 *)
  • PARI
    is(n)=gcd(n,10)==1 && znorder(Mod(-100, n))==n-1 \\ Charles R Greathouse IV, Mar 01 2025
  • PARI
    list(lim)=my(v=List([3])); forprime(p=7,lim, if(znorder(Mod(-100, p))==p-1, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Mar 01 2025
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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