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 11-20 of 20 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[#] &]

A158248 Composite numbers with primitive root 10.

Original entry on oeis.org

49, 289, 343, 361, 529, 841, 2209, 2401, 3481, 3721, 4913, 6859, 9409, 11881, 12167, 12769, 16807, 17161, 22201, 24389, 27889, 32041, 32761, 37249, 49729, 52441, 54289, 66049, 69169, 72361, 83521, 97969
Offset: 1

Views

Author

Robert Hutchins, Mar 15 2009

Keywords

Comments

Previous name was: Numbers m whose reciprocal generates a repeating decimal fraction with period phi(m) and m/2 < phi(m) < m-1.
All terms are proper powers of full reptend primes (A001913).
This sequence does not contain every proper power of every term in A001913, for example, A001913 has 487 as its 26th term, but since 10 is not a primitive root of 487^2, 487^2 is not a term of this sequence. - Robert Hutchins, Oct 14 2021
A shorter description appears to be "Composite numbers with primitive root 10". - Arkadiusz Wesolowski, Jul 04 2012 (The two definitions certainly produce the same terms up through 83521. - N. J. A. Sloane, Jul 05 2012)

Links

Crossrefs

Cf. A007732, A001913, A046145, A046146.
Subsequence of A244623.
Subsequence of A167797.
Cf. A108989 (for base 2), A346316 (for base 6).

Programs

  • Maple
    select(n -> not isprime(n) and numtheory:-primroot(9,n) = 10,[$2..10000]);
# N. J. A. Sloane, Jul 05 2012
  • Mathematica
    Select[Range[10^5], GCD[10, #] == 1 && #/2 < MultiplicativeOrder[10, #] < # - 1 &] (* Ray Chandler, Oct 17 2012 *)

Extensions

More terms from Robert Hutchins, Mar 21 2009
Entry revised by N. J. A. Sloane, Jul 05 2012
New name (using comment by Arkadiusz Wesolowski) from Joerg Arndt, Nov 22 2021

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 *)

A218766 Composite numbers with both 10 and -10 as primitive root.

Original entry on oeis.org

289, 841, 3721, 4913, 9409, 11881, 12769, 22201, 24389, 32761, 37249, 52441, 54289, 66049, 72361, 83521, 97969, 113569, 151321, 187489, 212521, 226981, 259081, 292681, 332929, 351649, 491401, 502681, 674041, 707281, 734449, 877969, 885481, 908209, 912673
Offset: 1

Views

Author

Arkadiusz Wesolowski, Nov 05 2012

Keywords

Comments

The powers of primes from A007349.
Intersection of A002808, A167797 and A167806.

Examples

			12769 = 113^2 belongs to this sequence because 113 is in A007349.

Links

Crossrefs

Cf. A007349.

Programs

  • Mathematica
    lst = {}; r = 912673; Do[If[PrimeQ[i] && MultiplicativeOrder[10, i] == MultiplicativeOrder[-10, i] == i - 1, n = 2; While[(p = i^n) <= r, AppendTo[lst, p]; n++]], {i, Floor@Sqrt[r]}]; Sort[lst]
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