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 10 results.

A116629 Positive integers k such that 13^k == 3 (mod k).

Original entry on oeis.org

1, 2, 5, 166, 287603, 9241538, 2366680105, 8347156585, 21682897793, 6988245760865, 9045859950329, 10076294257985, 50299408064905, 254874726648713
Offset: 1

Views

Author

Zak Seidov, Feb 19 2006

Keywords

Comments

No other terms below 10^15. - Max Alekseyev, Nov 24 2017
Some larger terms: 1440926367749746685, 76025040962646716305439353859479569558065. - Max Alekseyev, Jun 29 2011

Crossrefs

Cf. A116609, A050259, A122780, A130422, A123061, A277554.
Solutions to 13^n == k (mod n): A001022 (k=0), A015963 (k=-1), A116621 (k=1), A116622 (k=2), this sequence (k=3), A116630 (k=4), A116611 (k=5), A116631 (k=6), A116632 (k=7), A295532 (k=8), A116636 (k=9), A116620 (k=10), A116638 (k=11), A116639 (k=15).

Programs

  • Mathematica
    Join[{1, 2}, Select[Range[1, 5000], Mod[13^#, #] == 3 &]] (* G. C. Greubel, Nov 19 2017 *)
Join[{1, 2}, Select[Range[10000000], PowerMod[13, #, #] == 3 &]] (* Robert Price, Apr 10 2020 *)
  • PARI
    isok(n) = Mod(13, n)^n == 3; \\ Michel Marcus, Nov 19 2017

Extensions

Two more terms from Ryan Propper, Jan 09 2008
Terms 1,2 are prepended and a(9)-a(14) are added by Max Alekseyev, Jun 29 2011; Nov 24 2017

A123047 Numbers k that divide 5^k + 4.

Original entry on oeis.org

1, 3, 129, 60767, 76433163, 454034821, 26675718567, 164304369911289
Offset: 1

Views

Author

Alexander Adamchuk, Nov 04 2006

Keywords

Comments

k must be odd since any power of 5 plus 4 is odd. - Robert G. Wilson v, Nov 14 2006
a(9) > 10^15. - Max Alekseyev, Oct 17 2016
Large term (may not be the next one): 3014733401203184049549. - Max Alekseyev, Oct 18 2013

Crossrefs

Solutions to 5^n == k (mod n): A067946 (k=1), A015951 (k=-1), A124246 (k=2), A123062 (k=-2), A123061 (k=3), A123052 (k=-3), A125949 (k=4), this sequence (k=-4), A123091 (k=5), A015891 (k=-5), A277350 (k=6), A277348 (k=-6).

Programs

Extensions

a(4) and a(5) from Robert G. Wilson v, Nov 14 2006
a(7) from Ryan Propper, Mar 23 2007
a(8) from Max Alekseyev, Oct 17 2016

A123062 Numbers k that divide 5^k + 2.

Original entry on oeis.org

1, 7, 51373, 78127, 138943, 620299, 2842933, 137422693, 2259290321, 413879131637, 434757575329, 915535274009, 14864856896743
Offset: 1

Views

Author

Alexander Adamchuk, Nov 04 2006

Keywords

Comments

No further terms up to 10^15. Larger term: 64629734103979763971. - Max Alekseyev, Oct 15 2016

Crossrefs

Solutions to 5^n == k (mod n): A067946 (k=1), A015951 (k=-1), A124246 (k=2), this sequence (k=-2), A123061 (k=3), A123052 (k=-3), A125949 (k=4), A123047 (k=-4), A123091 (k=5), A015891 (k=-5), A277350 (k=6), A277348 (k=-6).

Programs

  • Mathematica
    Select[Range[1000000], IntegerQ[(PowerMod[5,#,# ]+2)/# ]&]
  • PARI
    is(n)=Mod(5,n)^n==-2 \\ Charles R Greathouse IV, Nov 04 2016

Extensions

More terms from Farideh Firoozbakht, Nov 18 2006
a(9) from Ryan Propper, Jan 29 2007
a(10)-a(13) from Max Alekseyev, Jul 28 2009, Oct 15 2016

A124246 Numbers k that divide 5^k - 2.

Original entry on oeis.org

1, 3, 123, 202884639, 242405133, 92273577267, 2670733723929, 81035221987959
Offset: 1

Views

Author

Farideh Firoozbakht, Nov 19 2006

Keywords

Comments

No other terms below 10^15. Some larger terms: 60092749466423900486673922957841, 401021769827858799355246286337987697472836927856337282726789534497163. - Max Alekseyev, Oct 15 2016

Crossrefs

Solutions to 5^n == k (mod n): A067946 (k=1), A015951 (k=-1), this sequence (k=2), A123062 (k=-2), A123061 (k=3), A123052 (k=-3), A125949 (k=4), A123047 (k=-4), A123091 (k=5), A015891 (k=-5), A277350 (k=6), A277348 (k=-6).

Programs

  • Mathematica
    Do[If[Mod[(PowerMod[5,n,n]-2),n]==0,Print[n]],{n,1000000000}]
  • PARI
    is(n)=Mod(5,n)^n==2 \\ Charles R Greathouse IV, Nov 04 2016

Extensions

a(6)-a(8) from Max Alekseyev, Jul 28 2009, Jun 02 2010, Oct 15 2016

A123052 Numbers k that divide 5^k + 3.

Original entry on oeis.org

1, 2, 4, 14, 628, 11524, 16814, 188404, 441484, 2541014, 3984724, 172315684, 208268941, 40874725514, 280454588548, 489850370956, 1235856817732, 62479203805793, 95467808763364, 116016015619396, 396249210287836
Offset: 1

Views

Author

Alexander Adamchuk, Nov 04 2006

Keywords

Comments

No other terms below 10^15. A larger term: 783847656467936404. - Max Alekseyev, Oct 16 2016

Crossrefs

Solutions to 5^n == k (mod n): A067946 (k=1), A015951 (k=-1), A124246 (k=2), A123062 (k=-2), A123061 (k=3), this sequence (k=-3), A125949 (k=4), A123047 (k=-4), A123091 (k=5), A015891 (k=-5), A277350 (k=6), A277348 (k=-6).

Programs

  • Mathematica
    Select[Range[1000000], IntegerQ[(PowerMod[5,#,# ]+3)/# ]&]
  • PARI
    is(n)=Mod(5,n)^n==-3 \\ Charles R Greathouse IV, Apr 06 2014

Extensions

a(10)-a(13) from Ryan Propper, Dec 30 2006, Jan 02 2007
More terms from Lars Blomberg, Nov 25 2011
Terms a(14) onwards were reported incorrect by Toshitaka Suzuki, and have been deleted. - N. J. A. Sloane, Mar 18 2014
a(14)-a(17) from Toshitaka Suzuki, Mar 18 2014, Apr 03 2014
a(18)-a(21) from Max Alekseyev, Oct 16 2016

A125949 Numbers k that divide 5^k - 4.

Original entry on oeis.org

1, 4769, 8563651, 300414792131, 2353957351049, 15960089894129, 452045914836301, 657236915690111
Offset: 1

Views

Author

Alexander Adamchuk, Feb 04 2007

Keywords

Comments

No other terms below 10^15. - Max Alekseyev, Oct 17 2016

Crossrefs

Solutions to 5^n == k (mod n): A067946 (k=1), A015951 (k=-1), A124246 (k=2), A123062 (k=-2), A123061 (k=3), A123052 (k=-3), this sequence (k=4), A123047 (k=-4), A123091 (k=5), A015891 (k=-5), A277350 (k=6), A277348 (k=-6).

Programs

  • Mathematica
    a(1) = 1; Do[ If[ PowerMod[5, 2n - 1, 2n - 1] - 4 == 0, Print[2n - 1]], {n,10^9}]
  • PARI
    is(n)=Mod(5,n)^n==4 \\ Charles R Greathouse IV, May 15 2013

Extensions

a(4)-a(8) from Max Alekseyev, Jun 09 2010, Oct 17 2016

A277350 Positive integers n such that 5^n == 6 (mod n).

Original entry on oeis.org

1, 15853, 5520343, 111966563, 2232207889, 5551501871
Offset: 1

Views

Author

Seiichi Manyama, Oct 10 2016

Keywords

Comments

No other terms below 10^15. - Max Alekseyev, Oct 18 2016

Crossrefs

Cf. Solutions to 5^n == k (mod n): A277348 (k=-6), A015891 (k=-5), A123047 (k=-4), A123052 (k=-3), A123062 (k=-2), A015951 (k=-1), A067946 (k=1), A124246 (k=2), A123061 (k=3), A125949 (k=4), A123091 (k=5), this sequence (k=6).

Programs

A277348 Positive integers n such that n | (5^n + 6).

Original entry on oeis.org

1, 11, 341, 581337017, 7202608727, 27146455379, 1358496201131, 9843739213499, 172392038905691
Offset: 1

Views

Author

Seiichi Manyama, Oct 10 2016

Keywords

Comments

No other terms below 10^15. - Max Alekseyev, Oct 17 2016

Examples

			5^11 + 6 = 48828131 = 11 * 4438921, so 11 is a term.

Crossrefs

Cf. A066603.
Cf. Solutions to 5^n == k (mod n): this sequence (k=-6), A015891 (k=-5), A123047 (k=-4), A123052 (k=-3), A123062 (k=-2), A015951 (k=-1), A067946 (k=1), A124246 (k=2), A123061 (k=3), A125949 (k=4), A123091 (k=5), A277350 (k=6).

Programs

  • PARI
    isok(n) = Mod(5, n)^n == -6; \\ Michel Marcus, Oct 10 2016

Formula

A066603(a(n)) = a(n) - 6 for n > 1.

Extensions

a(5)-a(9) from Max Alekseyev, Oct 17 2016

A277554 Positive integers n such that 7^n == 3 (mod n).

Original entry on oeis.org

1, 2, 46, 2227, 6684830083, 12827743861, 151652531182, 155657642297, 3102126273955, 11006109076099, 50473807426174, 172794904196354
Offset: 1

Views

Author

Max Alekseyev, Oct 19 2016

Keywords

Comments

No other terms below 10^15.

Crossrefs

Cf. A066438, A277126.
Cf. Solutions to 7^n == k (mod n): A277371 (k=-3), A277370 (k=-2), A015954 (k=-1), A067947 (k=1), A277401 (k=2).
Cf. Solutions to b^n == 3 (mod n): A050259 (b=2), A130422 (b=4), A123061 (b=5), A116629 (b=13).

Programs

A125285 Numbers n such that 11*n | 5^n - 3.

Original entry on oeis.org

2, 7, 22, 4157, 6677, 10207, 926527, 2814427, 35452202
Offset: 1

Views

Author

Zak Seidov, Nov 26 2006

Keywords

Examples

			5^22-3=22*108372081409801,
5^77-3=77*8594084286265222596066583813713899777307138814554586.

Crossrefs

Cf. A123061 = n | 5^n - 3.
Showing 1-10 of 10 results.

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

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