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

A116622 Positive integers n such that 13^n == 2 (mod n).

Original entry on oeis.org

1, 11, 140711, 863101, 1856455, 115602923, 566411084209, 706836043419179
Offset: 1

Views

Author

Zak Seidov, Feb 19 2006

Keywords

Comments

No other terms below 10^16. - Max Alekseyev, Nov 02 2018

Crossrefs

Cf. A116609.
Solutions to b^n == 2 (mod n): A015919 (b=2), A276671 (b=3), A130421 (b=4), A124246 (b=5), A277401 (b=7), this sequence (b=13), A333269 (b=17).
Solutions to 13^n == k (mod n): A015963 (k=-1), A116621 (k=1), this sequence (k=2), A116629 (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
    Select[Range[1, 500000], Mod[13^#, #] == 2 &] (* G. C. Greubel, Nov 19 2017 *)
Join[{1}, Select[Range[5000000], PowerMod[13, #, #] == 2 &]] (* Robert Price, Apr 10 2020 *)
  • PARI
    isok(n) = Mod(13, n)^n == 2; \\ Michel Marcus, Nov 19 2017

Extensions

One more term from Ryan Propper, Jun 11 2006
Term a(1)=1 is prepended and a(7)-a(8) are added by Max Alekseyev, Jun 29 2011

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

A123061 Numbers k that divide 5^k - 3.

Original entry on oeis.org

1, 2, 22, 77, 242, 371, 16102, 45727, 73447, 81286, 112277, 368237, 10191797, 13563742, 30958697, 389974222, 6171655457, 55606837682, 401469524477, 434715808966, 1729670231597, 12399384518278, 28370781933478, 32458602019394, 45360785149757, 1073804398767214
Offset: 1

Views

Author

Alexander Adamchuk, Nov 04 2006

Keywords

Comments

Some larger terms: 10157607413638637338691, 678641208236297002873422185407157785099272404809011007522511134591325167. - Max Alekseyev, Oct 20 2016

Crossrefs

Cf. A050259, A130422, A277554, A116629.
Solutions to 5^n == k (mod n): A067946 (k=1), A015951 (k=-1), A124246 (k=2), A123062 (k=-2), this sequence (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,#,# ]-3)/# ]&]
Do[If[IntegerQ[(PowerMod[5, n, n ]-3)/n], Print[n]], {n, 10^9}] (* Ryan Propper, Dec 30 2006 *)
  • PARI
    is(n)=Mod(5,n)^n==3 \\ Charles R Greathouse IV, Nov 04 2016

Extensions

More terms from Farideh Firoozbakht, Nov 18 2006
Corrected and extended by Ryan Propper, Jan 01 2007
Entry revised by N. J. A. Sloane, Jan 24 2007
a(18) from Lars Blomberg, Dec 12 2011
a(19)-a(26) from Max Alekseyev, Oct 20 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

A277401 Positive integers n such that 7^n == 2 (mod n).

Original entry on oeis.org

1, 5, 143, 1133, 2171, 8567, 16805, 208091, 1887043, 517295383, 878436591673
Offset: 1

Views

Author

Seiichi Manyama, Oct 13 2016

Keywords

Comments

All terms are odd.
No other terms below 10^15. Some larger terms: 181204957971619289, 21305718571846184078167, 157*(7^157-2)/1355 (132 digits). - Max Alekseyev, Oct 18 2016

Examples

			7 == 2 mod 1, so 1 is a term;
16807 == 2 mod 5, so 5 is a term.

Crossrefs

Cf. A066438.
Cf. Solutions to 7^n == k (mod n): A277371 (k=-3), A277370 (k=-2), A015954 (k=-1), A067947 (k=1), this sequence (k=2), A277554 (k=3).
Cf. Solutions to b^n == 2 (mod n): A015919 (b=2), A276671 (b=3), A130421 (b=4), A124246 (b=5), this sequence (b=7), A116622 (b=13).

Programs

  • Mathematica
    Join[{1},Select[Range[5173*10^5],PowerMod[7,#,#]==2&]] (* The program will generate the first 10 terms of the sequence; it would take a very long time to generate the 11th term. *) (* Harvey P. Dale, Apr 15 2020 *)
  • PARI
    isok(n) = Mod(7, n)^n == 2; \\ Michel Marcus, Oct 13 2016

Formula

A066438(a(n)) = 2 for n > 1.

Extensions

a(10) from Michel Marcus, Oct 13 2016
a(11) from Max Alekseyev, Oct 18 2016

A333269 Positive integers n such that 17^n == 2 (mod n).

Original entry on oeis.org

1, 3, 5, 3585, 4911, 5709, 1688565, 7361691, 16747709, 3226850283899, 8814126944005, 33226030397603
Offset: 1

Views

Author

Seiichi Manyama, Mar 14 2020

Keywords

Comments

No other terms below 10^16. Some larger term: 95549099691107109423357503242294996525424418266995858732192019626694044445113. - Max Alekseyev, Jan 09 2025

Crossrefs

Cf. Solutions to b^n == 2 (mod n): A015919 (b=2), A276671 (b=3), A130421 (b=4), A124246 (b=5), A277401 (b=7), A116622 (b=13), this sequence (b=17).

Programs

  • PARI
    for(k=1, 1e6, if(Mod(17, k)^k==2, print1(k", ")))
  • Python
    A333269_list = [n for n in range(1,10**6) if n == 1 or pow(17,n,n) == 2] # Chai Wah Wu, Mar 14 2020

Extensions

a(10)-a(12) from Max Alekseyev, Jan 09 2025
Showing 1-10 of 11 results. Next

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

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