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 1-9 of 9 results.

A380482 a(n) is the multiplicative order of -3 modulo prime(n); a(2) = 0 for completion.

Original entry on oeis.org

1, 0, 4, 3, 10, 6, 16, 9, 22, 28, 15, 9, 8, 21, 46, 52, 58, 5, 11, 70, 12, 39, 82, 88, 48, 100, 17, 106, 54, 112, 63, 130, 136, 69, 148, 25, 39, 81, 166, 172, 178, 90, 190, 16, 196, 99, 105, 111, 226, 114, 232, 238, 120, 250, 256, 262, 268, 15, 138, 280
Offset: 1

Views

Author

Jianing Song, Jun 27 2025

Keywords

Links

Crossrefs

Cf. A105875 (primes having primitive root -3).
Cf. bases 2..10: A014664, A062117, A082654, A211241, A211242, A211243, A211244, A211245, A002371.
Cf. bases -2..-10: A337878 (if first term 1), this sequence, A380531, A380532, A380533, A380540, A380541, A380542, A385222.

Programs

  • Mathematica
    A380482[n_] := If[n == 2, 0, MultiplicativeOrder[-3, Prime[n]]];
Array[A380482, 100] (* Paolo Xausa, Jun 29 2025 *)
  • PARI
    a(n,{k=-3}) = my(p = prime(n)); if(k%p==0, 0, znorder(Mod(k,p)))

A380531 a(n) is the multiplicative order of -4 modulo prime(n); a(1) = 0 for completion.

Original entry on oeis.org

0, 2, 1, 6, 10, 3, 4, 18, 22, 7, 10, 9, 5, 14, 46, 13, 58, 15, 66, 70, 18, 78, 82, 22, 24, 25, 102, 106, 9, 7, 14, 130, 17, 138, 37, 30, 13, 162, 166, 43, 178, 45, 190, 48, 49, 198, 210, 74, 226, 19, 58, 238, 12, 50, 8, 262, 67, 270, 23, 70
Offset: 1

Views

Author

Jianing Song, Jun 27 2025

Keywords

Comments

a(n) divides (p-1)/4 if p = prime(n) == 1 (mod 4), since (-4)^((p-1)/4) == (+-1+-i)^(p-1) == 1 (mod p), where i^2 == -1 (mod p).

Links

Crossrefs

Cf. A105876 (primes having primitive root -4).
Cf. bases 2..10: A014664, A062117, A082654, A211241, A211242, A211243, A211244, A211245, A002371.
Cf. bases -2..-10: A337878 (if first term 1), A380482, this sequence, A380532, A380533, A380540, A380541, A380542, A385222.

Programs

  • Mathematica
    A380531[n_] := If[n == 1, 0, MultiplicativeOrder[-4, Prime[n]]];
Array[A380531, 100] (* Paolo Xausa, Jun 29 2025 *)
  • PARI
    a(n,{k=-4}) = my(p = prime(n)); if(k%p==0, 0, znorder(Mod(k,p)))

A380532 a(n) is the multiplicative order of -5 modulo prime(n); a(3) = 0 for completion.

Original entry on oeis.org

1, 1, 0, 3, 10, 4, 16, 18, 11, 7, 6, 36, 20, 21, 23, 52, 58, 15, 11, 10, 72, 78, 41, 44, 96, 50, 51, 53, 54, 112, 21, 130, 136, 138, 74, 150, 156, 27, 83, 172, 178, 30, 38, 192, 196, 66, 70, 111, 113, 57, 232, 238, 40, 50, 256, 131, 134, 54, 276, 140
Offset: 1

Views

Author

Jianing Song, Jun 27 2025

Keywords

Links

Crossrefs

Cf. A105877 (primes having primitive root -5).
Cf. bases 2..10: A014664, A062117, A082654, A211241, A211242, A211243, A211244, A211245, A002371.
Cf. bases -2..-10: A337878 (if first term 1), A380482, A380531, this sequence, A380533, A380540, A380541, A380542, A385222.

Programs

  • Mathematica
    A380532[n_] := If[n == 3, 0, MultiplicativeOrder[-5, Prime[n]]];
Array[A380532, 100] (* Paolo Xausa, Jun 29 2025 *)
  • PARI
    a(n,{k=-5}) = my(p = prime(n)); if(k%p==0, 0, znorder(Mod(k,p)))

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

Views

Author

Jianing Song, Jun 27 2025

Keywords

Links

Crossrefs

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.

Programs

  • Mathematica
    A380533[n_] := If[n < 3, 0, MultiplicativeOrder[-6, Prime[n]]];
Array[A380533, 100] (* Paolo Xausa, Jun 29 2025 *)
  • PARI
    a(n,{k=-6}) = my(p = prime(n)); if(k%p==0, 0, znorder(Mod(k,p)))

A380540 a(n) is the multiplicative order of -7 modulo prime(n); a(4) = 0 for completion.

Original entry on oeis.org

1, 2, 4, 0, 5, 12, 16, 6, 11, 14, 30, 18, 40, 3, 46, 13, 58, 60, 33, 35, 24, 39, 82, 88, 96, 100, 102, 53, 54, 7, 63, 130, 68, 138, 37, 75, 52, 81, 166, 172, 89, 12, 5, 24, 49, 198, 105, 74, 226, 228, 116, 119, 240, 250, 256, 131, 268, 270, 69, 20
Offset: 1

Views

Author

Jianing Song, Jun 27 2025

Keywords

Links

Crossrefs

Cf. A105879 (primes having primitive root -7).
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, this sequence, A380541, A380542, A385222.

Programs

  • Mathematica
    A380540[n_] := If[n == 4, 0, MultiplicativeOrder[-7, Prime[n]]];
Array[A380540, 100] (* Paolo Xausa, Jun 29 2025 *)
  • PARI
    a(n,{k=-7}) = my(p = prime(n)); if(k%p==0, 0, znorder(Mod(k,p)))

A380541 a(n) is the multiplicative order of -8 modulo prime(n); a(1) = 0 for completion.

Original entry on oeis.org

0, 1, 4, 2, 5, 4, 8, 3, 22, 28, 10, 12, 20, 7, 46, 52, 29, 20, 11, 70, 6, 26, 41, 22, 16, 100, 34, 53, 12, 28, 14, 65, 68, 23, 148, 10, 52, 27, 166, 172, 89, 60, 190, 32, 196, 66, 35, 74, 113, 76, 58, 238, 8, 25, 16, 262, 268, 90, 92, 35
Offset: 1

Views

Author

Jianing Song, Jun 27 2025

Keywords

Links

Crossrefs

Cf. A105880 (primes having primitive root -8).
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, this sequence, A380542, A385222.

Programs

  • Mathematica
    A380541[n_] := If[n == 1, 0, MultiplicativeOrder[-8, Prime[n]]];
Array[A380541, 100] (* Paolo Xausa, Jun 29 2025 *)
  • PARI
    a(n,{k=-8}) = my(p = prime(n)); if(k%p==0, 0, znorder(Mod(k,p)))

Formula

a(n) = ord(-2,p)/gcd(ord(-2,p),3) for p != 2, where p = prime(n), and ord(a,m) is the multiplicative order of a modulo m. Note that ord(-2,p) = A337878(n) for n > 2.

A380542 a(n) is the multiplicative order of -9 modulo prime(n); a(2) = 0 for completion.

Original entry on oeis.org

1, 0, 1, 6, 10, 6, 8, 18, 22, 7, 30, 18, 4, 42, 46, 13, 58, 10, 22, 70, 3, 78, 82, 44, 24, 25, 34, 106, 54, 56, 126, 130, 68, 138, 37, 50, 78, 162, 166, 43, 178, 90, 190, 8, 49, 198, 210, 222, 226, 114, 116, 238, 60, 250, 128, 262, 67, 30, 138, 140
Offset: 1

Views

Author

Jianing Song, Jun 27 2025

Keywords

Links

Crossrefs

Cf. A105881 (primes having primitive root -9).
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, this sequence, A385222.

Programs

  • Mathematica
    A380542[n_] := If[n == 2, 0, MultiplicativeOrder[-9, Prime[n]]];
Array[A380542, 100] (* Paolo Xausa, Jun 29 2025 *)
  • PARI
    a(n,{k=-9}) = my(p = prime(n)); if(k%p==0, 0, znorder(Mod(k,p)))

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)))

A385228 Odd multiplicative orders of -2 modulo primes.

Original entry on oeis.org

1, 5, 9, 7, 29, 33, 41, 53, 65, 69, 81, 89, 105, 113, 25, 35, 47, 51, 15, 173, 189, 209, 221, 233, 245, 83, 261, 273, 281, 57, 293, 77, 309, 107, 329, 11, 115, 123, 393, 135, 413, 429, 441, 453, 473, 97, 509, 129, 131, 175, 545, 137, 561, 83, 585, 593, 149, 629, 641, 645, 653, 713, 725
Offset: 1

Views

Author

Jianing Song, Jun 22 2025

Keywords

Comments

a(n) is the multiplicative order of -2 modulo A163183(n).
Odd elements in A337878 (with first term changed to 1).

Links

Crossrefs

Cf. A337878, A163183 (corresponding primes).
Cf. other bases: A139686 (base 2), A385226 (base 3), A385227 (base 4), A385193 (base 5), this sequence (base -2), A385229 (base -3), A385230 (base -4), A385231 (base -5).

Programs

  • Mathematica
    Select[Map[MultiplicativeOrder[-2, #] &, Prime[Range[250]]], OddQ] (* Paolo Xausa, Jun 28 2025 *)
  • PARI
    forprime(p=3, 1e4, z=znorder(Mod(-2, p)); if(z%2, print1(z, ", ")))
Showing 1-9 of 9 results.

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