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.

Previous Showing 11-19 of 19 results.

A240100 Numbers with primitive root -17.

Original entry on oeis.org

2, 4, 5, 10, 19, 25, 37, 38, 41, 43, 47, 50, 59, 61, 67, 74, 82, 83, 86, 94, 97, 103, 113, 118, 122, 125, 127, 134, 151, 166, 173, 179, 191, 193, 194, 197, 206, 226, 233, 239, 250, 251, 254, 263, 269, 271, 277, 302, 313, 317, 331, 346, 358, 359, 361, 382
Offset: 1

Views

Author

Vincenzo Librandi, Apr 01 2014

Keywords

Links

Crossrefs

Cf. numbers with positive primitive root r: A167791 (r=2), A167792 (r=3), A167793 (r=5), A167794 (r=6), A167795 (r=7), A167796 (r=8), A167797 (r=10), A240028 (r=11), A240030 (r=12), A240032 (r=13), A240094 (r=14), A240096 (r=15), A240101 (r=17).
Cf. numbers with negative primitive root r: A167798 (r=-2), A167799 (r=-3), A167800 (r=-4), A167801 (r=-5), A167802 (r=-6), A167803 (r=-7), A167804 (r=-8), A167805 (r=-9), A167806 (r=-10), A240029 (r=-11), A240031 (r=-12), A240093 (r=-13), A240095 (r=-14), A240097 (r=-15).

Programs

  • Mathematica
    pr = -17; Select[Range[2, 400], MultiplicativeOrder[pr, #] == EulerPhi[#] &]

A240102 Numbers with primitive root -18.

Original entry on oeis.org

5, 7, 23, 29, 31, 37, 47, 53, 61, 71, 101, 103, 109, 127, 149, 151, 157, 167, 173, 181, 191, 197, 223, 239, 263, 269, 271, 277, 293, 317, 349, 359, 367, 383, 389, 397, 421, 461, 479, 503, 509, 529, 541, 557, 607, 613, 647, 653, 661, 677, 701, 719, 733
Offset: 1

Views

Author

Vincenzo Librandi, Apr 01 2014

Keywords

Links

Crossrefs

Cf. numbers with positive primitive root r: A167791 (r=2), A167792 (r=3), A167793 (r=5), A167794 (r=6), A167795 (r=7), A167796 (r=8), A167797 (r=10), A240028 (r=11), A240030 (r=12), A240032 (r=13), A240094 (r=14), A240096 (r=15), A240101 (r=17), A240103 (r=18).
Cf. numbers with negative primitive root r: A167798 (r=-2), A167799 (r=-3), A167800 (r=-4), A167801 (r=-5), A167802 (r=-6), A167803 (r=-7), A167804 (r=-8), A167805 (r=-9), A167806 (r=-10), A240029 (r=-11), A240031 (r=-12), A240093 (r=-13), A240095 (r=-14), A240097 (r=-15), A240100 (r=-17).

Programs

  • Mathematica
    pr = -18; Select[Range[2, 800], MultiplicativeOrder[pr, #] == EulerPhi[#] &]
  • PARI
    is(n)=if(gcd(n,6)>1, return(0)); my(p=eulerphi(n)); znorder(Mod(-18,n),p)==p \\ Charles R Greathouse IV, Nov 26 2014

A240103 Numbers with primitive root 18.

Original entry on oeis.org

5, 11, 29, 37, 43, 53, 59, 61, 67, 83, 101, 107, 109, 121, 139, 149, 157, 163, 173, 179, 181, 197, 227, 251, 269, 277, 283, 293, 317, 347, 349, 379, 389, 397, 419, 421, 461, 467, 491, 509, 523, 541, 547, 557, 563, 571, 587, 613, 619, 653, 659, 661, 677
Offset: 1

Views

Author

Vincenzo Librandi, Apr 01 2014

Keywords

Links

Crossrefs

Cf. numbers with positive primitive root r: A167791 (r=2), A167792 (r=3), A167793 (r=5), A167794 (r=6), A167795 (r=7), A167796 (r=8), A167797 (r=10), A240028 (r=11), A240030 (r=12), A240032 (r=13), A240094 (r=14), A240096 (r=15), A240101 (r=17).
Cf. numbers with negative primitive root r: A167798 (r=-2), A167799 (r=-3), A167800 (r=-4), A167801 (r=-5), A167802 (r=-6), A167803 (r=-7), A167804 (r=-8), A167805 (r=-9), A167806 (r=-10), A240029 (r=-11), A240031 (r=-12), A240093 (r=-13), A240095 (r=-14), A240097 (r=-15), A240100 (r=-17), A240102 (r=-18).

Programs

  • Mathematica
    pr = 18; Select[Range[2, 800], MultiplicativeOrder[pr, #] == EulerPhi[#] &]
  • PARI
    is(n)=if(gcd(n, 6)>1, return(0)); my(p=eulerphi(n)); znorder(Mod(18, n), p)==p \\ Charles R Greathouse IV, Nov 26 2014

A240101 Numbers with primitive root 17.

Original entry on oeis.org

2, 3, 5, 6, 7, 10, 11, 14, 22, 23, 25, 31, 37, 41, 46, 49, 50, 61, 62, 74, 82, 97, 98, 107, 113, 121, 122, 125, 131, 139, 167, 173, 193, 194, 197, 211, 214, 226, 227, 233, 242, 250, 262, 269, 277, 278, 283, 311, 313, 317, 334, 343, 346, 347, 367, 379, 386
Offset: 1

Views

Author

Vincenzo Librandi, Apr 01 2014

Keywords

Links

Crossrefs

Cf. numbers with positive primitive root r: A167791 (r=2), A167792 (r=3), A167793 (r=5), A167794 (r=6), A167795 (r=7), A167796 (r=8), A167797 (r=10), A240028 (r=11), A240030 (r=12), A240032 (r=13), A240094 (r=14), A240096 (r=15).
Cf. numbers with negative primitive root r: A167798 (r=-2), A167799 (r=-3), A167800 (r=-4), A167801 (r=-5), A167802 (r=-6), A167803 (r=-7), A167804 (r=-8), A167805 (r=-9), A167806 (r=-10), A240029 (r=-11), A240031 (r=-12), A240093 (r=-13), A240095 (r=-14), A240097 (r=-15), A240100 (r=-17).

Programs

  • Mathematica
    pr = 17; Select[Range[2, 400], MultiplicativeOrder[pr, #] == EulerPhi[#] &]

A240104 Numbers with primitive root -19.

Original entry on oeis.org

2, 3, 6, 13, 26, 29, 31, 37, 41, 53, 58, 59, 62, 67, 71, 74, 79, 82, 89, 103, 106, 107, 113, 118, 134, 142, 158, 167, 173, 178, 179, 193, 206, 214, 223, 226, 227, 257, 269, 281, 293, 317, 331, 334, 337, 346, 358, 379, 383, 386, 401, 431, 433, 439, 446, 449
Offset: 1

Views

Author

Vincenzo Librandi, Apr 01 2014

Keywords

Links

Crossrefs

Cf. numbers with positive primitive root r: A167791 (r=2), A167792 (r=3), A167793 (r=5), A167794 (r=6), A167795 (r=7), A167796 (r=8), A167797 (r=10), A240028 (r=11), A240030 (r=12), A240032 (r=13), A240094 (r=14), A240096 (r=15), A240101 (r=17), A240103 (r=18), A240106 (r=19).
Cf. numbers with negative primitive root r: A167798 (r=-2), A167799 (r=-3), A167800 (r=-4), A167801 (r=-5), A167802 (r=-6), A167803 (r=-7), A167804 (r=-8), A167805 (r=-9), A167806 (r=-10), A240029 (r=-11), A240031 (r=-12), A240093 (r=-13), A240095 (r=-14), A240097 (r=-15), A240100 (r=-17), A240102 (r=-18).

Programs

  • Mathematica
    pr = -19; Select[Range[2, 500], MultiplicativeOrder[pr, #] == EulerPhi[#] &]

A240106 Numbers with primitive root 19.

Original entry on oeis.org

2, 4, 7, 11, 13, 14, 22, 23, 26, 29, 37, 41, 43, 46, 47, 53, 58, 74, 82, 83, 86, 89, 94, 106, 113, 121, 139, 163, 166, 173, 178, 191, 193, 226, 239, 242, 251, 257, 263, 269, 278, 281, 293, 311, 317, 326, 337, 346, 347, 359, 367, 382, 386, 401, 419, 433, 443
Offset: 1

Views

Author

Vincenzo Librandi, Apr 01 2014

Keywords

Links

Crossrefs

Cf. numbers with positive primitive root r: A167791 (r=2), A167792 (r=3), A167793 (r=5), A167794 (r=6), A167795 (r=7), A167796 (r=8), A167797 (r=10), A240028 (r=11), A240030 (r=12), A240032 (r=13), A240094 (r=14), A240096 (r=15), A240100 (r=17), A240103 (r=18).
Cf. numbers with negative primitive root r: A167798 (r=-2), A167799 (r=-3), A167800 (r=-4), A167801 (r=-5), A167802 (r=-6), A167803 (r=-7), A167804 (r=-8), A167805 (r=-9), A167806 (r=-10), A240029 (r=-11), A240031 (r=-12), A240093 (r=-13), A240095 (r=-14), A240097 (r=-15), A240100 (r=-17), A240102 (r=-18), A240104 (r=-19).

Programs

  • Mathematica
    pr = 19; Select[Range[2, 500], MultiplicativeOrder[pr, #] == EulerPhi[#] &]

A240107 Numbers with primitive root -20.

Original entry on oeis.org

11, 13, 17, 31, 37, 53, 59, 73, 79, 113, 121, 131, 137, 139, 157, 169, 173, 179, 191, 199, 211, 233, 239, 257, 271, 277, 289, 293, 313, 317, 331, 337, 353, 359, 379, 397, 419, 431, 433, 439, 479, 499, 557, 593, 599, 613, 631, 653, 659, 673, 677, 719, 751
Offset: 1

Views

Author

Vincenzo Librandi, Apr 01 2014

Keywords

Links

Crossrefs

Cf. numbers with positive primitive root r: A167791 (r=2), A167792 (r=3), A167793 (r=5), A167794 (r=6), A167795 (r=7), A167796 (r=8), A167797 (r=10), A240028 (r=11), A240030 (r=12), A240032 (r=13), A240094 (r=14), A240096 (r=15), A240100 (r=17), A240103 (r=18), A240106 (r=19), A240108 (r=20).
Cf. numbers with negative primitive root r: A167798 (r=-2), A167799 (r=-3), A167800 (r=-4), A167801 (r=-5), A167802 (r=-6), A167803 (r=-7), A167804 (r=-8), A167805 (r=-9), A167806 (r=-10), A240029 (r=-11), A240031 (r=-12), A240093 (r=-13), A240095 (r=-14), A240097 (r=-15), A240100 (r=-17), A240102 (r=-18), A240104 (r=-19).

Programs

  • Mathematica
    pr = -20; Select[Range[2, 800], MultiplicativeOrder[pr, #] == EulerPhi[#] &]

A240108 Numbers with primitive root 20.

Original entry on oeis.org

3, 9, 13, 17, 23, 27, 37, 43, 47, 53, 67, 73, 81, 83, 103, 107, 113, 137, 157, 163, 167, 169, 173, 223, 227, 233, 243, 257, 263, 277, 283, 289, 293, 313, 317, 337, 347, 353, 367, 383, 397, 433, 443, 463, 467, 487, 503, 529, 547, 557, 563, 587, 593, 607
Offset: 1

Views

Author

Vincenzo Librandi, Apr 01 2014

Keywords

Links

Crossrefs

Cf. numbers with positive primitive root r: A167791 (r=2), A167792 (r=3), A167793 (r=5), A167794 (r=6), A167795 (r=7), A167796 (r=8), A167797 (r=10), A240028 (r=11), A240030 (r=12), A240032 (r=13), A240094 (r=14), A240096 (r=15), A240100 (r=17), A240103 (r=18), A240106 (r=19).
Cf. numbers with negative primitive root r: A167798 (r=-2), A167799 (r=-3), A167800 (r=-4), A167801 (r=-5), A167802 (r=-6), A167803 (r=-7), A167804 (r=-8), A167805 (r=-9), A167806 (r=-10), A240029 (r=-11), A240031 (r=-12), A240093 (r=-13), A240095 (r=-14), A240097 (r=-15), A240100 (r=-17), A240102 (r=-18), A240104 (r=-19), A240107 (r=-20).

Programs

  • Mathematica
    pr = 20; Select[Range[2, 700], MultiplicativeOrder[pr, #] == EulerPhi[#] &]
Join[{3,9,13,17},Select[Range[610],MemberQ[PrimitiveRootList[#],20]&]] (* Harvey P. Dale, Jul 17 2025 *)

A346316 Composite numbers with primitive root 6.

Original entry on oeis.org

121, 169, 289, 1331, 1681, 2197, 3481, 3721, 4913, 6241, 6889, 7921, 10609, 11449, 11881, 12769, 14641, 16129, 17161, 18769, 22801, 24649, 28561, 32041, 39601, 49729, 51529, 52441, 54289, 63001, 66049, 68921, 73441, 76729, 83521, 120409, 134689, 139129, 157609
Offset: 1

Views

Author

Robert Hutchins, Jul 13 2021

Keywords

Comments

An alternative description: Numbers k such that 1/k in base 6 generates a repeating fraction with period phi(n) and n/2 < phi(n) < n-1.
For example, in base 6, 1/121 has repeat length 110 = phi(121) which is > 121/2 but less than 121-1.

Links

Crossrefs

Subsequence of A244623.
Subsequence of A167794.
Cf. A108989 (for base 2), A158248 (for base 10).
Cf. A157502.

Programs

  • Maple
    isA033948 := proc(n)
    if n in {1,2,4} then
        true;
    elif type(n,'odd') and nops(numtheory[factorset](n)) = 1 then
        true;
    elif type(n,'even') and type(n/2,'odd') and nops(numtheory[factorset](n/2)) = 1 then
        true;
    else
        false;
    end if;
end proc:
isA167794 := proc(n)
    if not isA033948(n) or n = 1 then
        false;
    elif numtheory[order](6,n) = numtheory[phi](n) then
        true;
    else
        false;
    end if;
end proc:
A346316 := proc(n)
    option remember;
    local a;
    if n = 1 then
        121;
    else
        for a from procname(n-1)+1 do
            if not isprime(a) and isA167794(a) then
                return a;
            end if;
        end do:
    end if;
end proc:
seq(A346316(n),n=1..20) ; # R. J. Mathar, Sep 15 2021
  • Mathematica
    Select[Range[160000], CompositeQ[#] && PrimitiveRoot[#, 6] == 6 &] (* Amiram Eldar, Jul 13 2021 *)
  • PARI
    isok(m) = (m>1) && !isprime(m) && (gcd(m, 6)==1) && (znorder(Mod(6, m))==eulerphi(m)); \\ Michel Marcus, Aug 12 2021

Formula

A167794 INTERSECT A002808.
Previous Showing 11-19 of 19 results.

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