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 1-10 of 11 results. Next

A125645 Smallest odd prime base q such that p^4 divides q^(p-1) - 1, where p = prime(n).

Original entry on oeis.org

17, 163, 443, 3449, 45989, 239, 15541, 2819, 60793, 78017, 690143, 398023, 1977343, 574081, 1513367, 4388179, 3198427, 8065789, 3246107, 1353383, 5934307, 15631613, 2864371, 14754769, 15012733, 1358891, 32414783, 119551, 21860063, 11281097
Offset: 1

Views

Author

Alexander Adamchuk, Nov 29 2006

Keywords

Links

Crossrefs

Cf. A125609, A125610, A125611, A125612, A125632, A125633, A125634, A125635, A125636, A125637, A125646, A125647, A125648, A125649.

Programs

  • Maple
    f:= proc(n) local p, r, S,i,s,t;
  uses numtheory;
  p:= ithprime(n);
  r:= primroot(p^4);
  S:= sort([seq(r &^ (i*p^3) mod p^4, i=0..p-2)]);
  for i from 0 do
    for s in S do
      t:= i*p^4+s;
      if t::odd and isprime(t) then return t fi
  od od
end proc:
f(1):= 1:
map(f, [$1..100]); # Robert Israel, Feb 12 2017
  • PARI
    { a(n) = local(p,x,y); if(n==1,return(17)); p=prime(n); x=znprimroot(p^4)^(p^3); vecsort( vector(p-1,i, y=lift(x^i);while(!isprime(y),y+=p^4);y ) )[1] } \\ Max Alekseyev, May 30 2007

Extensions

More terms from Max Alekseyev, May 30 2007

A125648 Smallest odd prime base q such that p^7 divides q^(p-1) - 1, where p = Prime[n].

Original entry on oeis.org

257, 4373, 735443, 3294173, 28723679, 533810141, 38277341, 47579927, 982740799, 33956348611, 77141582851, 174329354539, 82984891817, 109051450427, 83209719751, 1352085061013, 171168499897, 1822904926391, 2870322429133, 3589197993463, 2603594622571, 5834621843669, 1411025860033, 20635686238253, 1580041060459, 26763849212297, 8216934406781, 28482190726739, 97876187600351
Offset: 1

Views

Author

Alexander Adamchuk, Nov 29 2006

Keywords

Links

Crossrefs

Cf. A125609, A125610, A125611, A125612, A125632, A125633, A125634, A125635, A125636, A125637, A125645, A125646, A125647, A125649.

Programs

  • PARI
    { a125648(n) = my(p, x, r); if(n==1, return(257)); p=prime(n); x=znprimroot(p^7)^(p^6); vecmin( vector(p-1, i, forprimestep(y=2,oo,x^i,r=y;break); r) ); } \\ Max Alekseyev, May 30 2007; updated Apr 01 2025

Extensions

More terms from Max Alekseyev, May 30 2007

A125647 Smallest odd prime base q such that p^6 divides q^(p-1) - 1, where p = Prime[n].

Original entry on oeis.org

193, 1459, 14557, 152617, 2120879, 7654109, 24527681, 2342959, 90603883, 1657641497, 40373093, 2175429661, 1614357949, 119612113, 14635471219, 2816276179, 15591204869, 1006953931, 7726467079, 48931161299, 54908441659, 41985419521, 583493688221, 200335697059, 96891225583, 50303508131, 129847013561, 362253784469, 625810253147, 195406393583
Offset: 1

Views

Author

Alexander Adamchuk, Nov 29 2006

Keywords

Links

Crossrefs

Cf. A125609, A125610, A125611, A125612, A125632, A125633, A125634, A125635, A125636, A125637, A125645, A125646, A125648, A125649.

Programs

  • PARI
    { a(n) = local(p,x,y); if(n==1,return(193)); p=prime(n); x=znprimroot(p^6)^(p^5); vecsort( vector(p-1,i, y=lift(x^i);while(!isprime(y),y+=p^6);y ) )[1] } \\ Max Alekseyev, May 30 2007

Extensions

More terms from Max Alekseyev, May 30 2007

A125649 Smallest odd prime base q such that p^8 divides q^(p-1) - 1, where p = prime(n).

Original entry on oeis.org

257, 13121, 3124999, 3376853, 174625993, 533810141, 16048035481, 3620189879, 982740799, 547344139109, 497929938133, 1105109875657, 15682480615619, 1391016035411, 83209719751, 84224951222611, 165554755409789, 254747341131683, 701000310909907, 317304132615017
Offset: 1

Views

Author

Alexander Adamchuk, Nov 29 2006

Keywords

Links

Crossrefs

Cf. A125609, A125610, A125611, A125612, A125632, A125633, A125634, A125635, A125636, A125637, A125645, A125646, A125647, A125648.

Programs

  • Mathematica
    Do[p = Prime[n]; q = 2; While[PowerMod[q, p-1, p^8] != 1, q = NextPrime[q]]; Print[q], {n, 100}] (* Ryan Propper, Apr 01 2007 *)
  • PARI
    { a(n) = local(p,x,y); if(n==1,return(257)); p=prime(n); x=znprimroot(p^8)^(p^7); vecsort( vector(p-1,i, y=lift(x^i);while(!isprime(y),y+=p^8);y ) )[1] } \\ Max Alekseyev, May 30 2007

Extensions

More terms from Ryan Propper, Apr 01 2007
More terms from Max Alekseyev, May 30 2007

A133859 Smallest odd prime base q such that p^9 divides q^(p-1) - 1, where p = prime(n).

Original entry on oeis.org

7681, 39367, 7812499, 135967277, 4715895383, 822557039, 48718117843, 513127081109, 147534349327, 21203414421907, 52879244321341, 15069267560119, 798099274499279, 164129642266943, 1740228634955257, 149381307185023
Offset: 1

Views

Author

Alexander Adamchuk, Sep 26 2007

Keywords

Examples

			a(1) = A035089(9) = 7681.
a(2) = A125609(9) = 39367.
a(3) = A125610(9) = 7812499.

Crossrefs

Cf. A035089, A125609, A125610, A125611, A125612, A125632, A125633, A125634, A125635, A125636, A125637, A125645, A125646, A125647, A125648, A125649, A133860, A133861, A133862, A133863, A133864, A133865.

Programs

  • Mathematica
    Do[ k = 1; While[ !PowerMod[ Prime[ k ], Prime[ n ] - 1, Prime[ n ]^9 ] == 1, k++ ]; Print[ { n, Prime[ k ] } ], {n, 1, 100} ]

Extensions

Extended by Max Alekseyev, May 08 2009

A133860 Smallest odd prime base q such that p^10 divides q^(p-1) - 1, where p = prime(n).

Original entry on oeis.org

12289, 472391, 78124999, 135967277, 24262286441, 38050596989, 5498076927457, 8388044818849, 30794280412669, 45941644105613, 1205285836084793, 7909086479714171, 1438991183761177, 47101607991825047, 18067554193458689
Offset: 1

Views

Author

Alexander Adamchuk, Sep 26 2007

Keywords

Examples

			a(1) = A035089(10) = 12289.

Crossrefs

Cf. A035089, A125609, A125610, A125611, A125612, A125632, A125633, A125634, A125635, A125636, A125637, A125645, A125646, A125647, A125648, A125649, A133859, A133861, A133862, A133863, A133864, A133865.

Programs

  • Mathematica
    Do[ k = 1; While[ !PowerMod[ Prime[ k ], Prime[ n ] - 1, Prime[ n ]^10 ] == 1, k++ ]; Print[ { n, Prime[ k ] } ], {n, 1, 100} ]

Extensions

Extended by Max Alekseyev, May 08 2009

A133861 Smallest odd prime base q such that p^11 divides q^(p-1) - 1, where p = prime(n).

Original entry on oeis.org

12289, 1062881, 292968749, 7909306973, 1194631280321, 2395794301259, 38413406256881, 77460384757423, 30794280412669, 4161130688896397, 3748333074529501, 240404931594746129, 191828075390557213
Offset: 1

Views

Author

Alexander Adamchuk, Sep 26 2007

Keywords

Examples

			a(1) = A035089(11) = 12289.

Crossrefs

Cf. A035089, A125609, A125610, A125611, A125612, A125632, A125633, A125634, A125635, A125636, A125637, A125645, A125646, A125647, A125648, A125649, A133859, A133860, A133862, A133863, A133864, A133865.

Programs

  • Mathematica
    Do[ k = 1; While[ !PowerMod[ Prime[ k ], Prime[ n ] - 1, Prime[ n ]^11 ] == 1, k++ ]; Print[ { n, Prime[ k ] } ], {n, 1, 100} ]

Extensions

Extended by Max Alekseyev, May 08 2009

A133862 Smallest odd prime base q such that p^12 divides q^(p-1) - 1, where p = prime(n).

Original entry on oeis.org

12289, 1062881, 853235443, 92233439147, 3143820659087, 58713568184837, 2359162908109223, 2649283656602003, 53928980532177631, 557792163777408809, 2084452633098194627, 8958368398788306367, 15810453676175767201
Offset: 1

Views

Author

Alexander Adamchuk, Sep 26 2007

Keywords

Examples

			a(1) = A035089(12) = 12289.

Crossrefs

Cf. A035089, A125609, A125610, A125611, A125612, A125632, A125633, A125634, A125635, A125636, A125637, A125645, A125646, A125647, A125648, A125649, A133859, A133860, A133861, A133863, A133864, A133865.

Programs

  • Mathematica
    Do[ k = 1; While[ !PowerMod[ Prime[ k ], Prime[ n ] - 1, Prime[ n ]^12 ] == 1, k++ ]; Print[ { n, Prime[ k ] } ], {n, 1, 100} ]

Extensions

Extended by Max Alekseyev, May 08 2009

A133863 Smallest odd prime base q such that p^13 divides q^(p-1) - 1, where p = prime(n).

Original entry on oeis.org

40961, 19131877, 2441406251, 115385868869, 138090848575723, 358661570404751, 44510586506850631, 252317900773542353, 4465433274456775633, 39171440762351329829, 11887418854442931407, 14582408526413537791
Offset: 1

Views

Author

Alexander Adamchuk, Sep 26 2007

Keywords

Examples

			a(1) = A035089(13) = 40961.

Crossrefs

Cf. A035089, A125609, A125610, A125611, A125612, A125632, A125633, A125634, A125635, A125636, A125637, A125645, A125646, A125647, A125648, A125649, A133859, A133860, A133861, A133862, A133864, A133865.

Programs

  • Mathematica
    Do[ k = 1; While[ !PowerMod[ Prime[ k ], Prime[ n ] - 1, Prime[ n ]^13 ] == 1, k++ ]; Print[ { n, Prime[ k ] } ], {n, 1, 100} ]

Extensions

Extended by Max Alekseyev, May 08 2009

A133864 Smallest odd prime base q such that p^14 divides q^(p-1) - 1, where p = prime(n).

Original entry on oeis.org

65537, 19131877, 53834264557, 1356446145697, 488581592070877, 22771419458231473, 346100334752156863, 2467410166021233673, 19165875476832528551, 61879867860030528131, 1106827928513014993387
Offset: 1

Views

Author

Alexander Adamchuk, Sep 26 2007

Keywords

Examples

			a(1) = A035089(14) = 65537.

Crossrefs

Cf. A035089, A125609, A125610, A125611, A125612, A125632, A125633, A125634, A125635, A125636, A125637, A125645, A125646, A125647, A125648, A125649, A133859, A133860, A133861, A133862, A133863, A133865.

Programs

  • Mathematica
    Do[ k = 1; While[ !PowerMod[ Prime[ k ], Prime[ n ] - 1, Prime[ n ]^14 ] == 1, k++ ]; Print[ { n, Prime[ k ] } ], {n, 1, 100} ]

Extensions

Extended by Max Alekseyev, May 08 2009
Showing 1-10 of 11 results. Next

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

Content is available under The OEIS End-User License Agreement.