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 1-7 of 7 results.

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

A015954 Numbers k such that k | 7^k + 1.

Original entry on oeis.org

1, 2, 10, 50, 250, 1250, 2810, 5050, 6250, 14050, 25250, 31250, 40210, 70250, 126250, 156250, 201050, 351250, 510050, 631250, 650050, 781250, 789610, 1005250, 1265050, 1419050, 1756250, 2550250, 3156250, 3250250, 3906250, 3948050, 5026250, 6325250, 7095250, 8781250, 9478130
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Links

Crossrefs

Solutions to b^k == -1 (mod k): A006521 (b=2), A015949 (b=3), A015950 (b=4), A015951 (b=5), A015953 (b=6), this sequence (b=7), A015955 (b=8), A015957 (b=9), A015958 (b=10), A015960 (b=11), A015961 (b=12), A015963 (b=13), A015965 (b=14), A015968 (b=15), A015969 (b=16).
Cf. A277370, A277401.
Column k=7 of A333429.

A277370 Positive integers k that divide 7^k + 2.

Original entry on oeis.org

1, 3, 15, 69, 2155, 34073, 876047637, 97090036327, 420397381695, 2125899832395, 3177544777277, 34434175473881, 40845965389135, 7267074621260963, 11720938824295035, 21419515204636141
Offset: 1

Views

Author

Seiichi Manyama, Oct 11 2016

Keywords

Comments

All terms are odd.
Some larger terms: 5623143546839445899891, 46186634668308298262543001. - Max Alekseyev, Oct 18 2016

Examples

			7^3 + 2 = 345 = 3 * 115, so 3 is a term.

Crossrefs

Cf. A066438.
Cf. Solutions to 7^n == k (mod n): A277371 (k=-3), this sequence (k=-2), A015954 (k=-1), A067947 (k=1), A277401 (k=2), A277554 (k=3).

Programs

  • Mathematica
    Select[Range[1, 9999, 2], Divisible[7^# + 2, #] &] (* Alonso del Arte, Oct 11 2016 *)
  • PARI
    is(n) = Mod(7, n)^n==-2 \\ Felix Fröhlich, Oct 14 2016

Formula

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

Extensions

a(8)-a(13) from Max Alekseyev, Oct 18 2016
a(14)-a(16) from Max Alekseyev, Dec 27 2024

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

A277371 Positive integers k that divide 7^k + 3.

Original entry on oeis.org

1, 2, 4, 5, 26, 205, 2404, 88171, 1785134, 2010899, 58796834, 639723359, 657788549, 2050134685, 4809019972, 6114530474, 11931055777, 1292089439947, 1294667166242, 4586221808305
Offset: 1

Views

Author

Seiichi Manyama, Oct 11 2016

Keywords

Comments

No other terms below 10^15. Some larger terms: 68363072121992414, 95409505835353571, 1579273736555455916822694118995172, 5481414795965035698701145369881812, 14905708205837180834697194210878924, 45415365018055454586462673640490785681840279, 147329898999183698422689397719859437775766016038732177717811807964. - Max Alekseyev, Oct 18 2016

Examples

			7^5 + 3 = 16810 = 5 * 3362, so 5 is a term.

Crossrefs

Cf. A066438.
Cf. Solutions to 7^n == k (mod n): this sequence (k=-3), A277370 (k=-2), A015954 (k=-1), A067947 (k=1), A277401 (k=2), A277554 (k=3).

Programs

  • Mathematica
    Select[Range[10000], Divisible[7^# + 3, #] &] (* Alonso del Arte, Oct 11 2016 *)
Join[{1,2},Select[Range[21*10^5],PowerMod[7,#,#]==#-3&]] (* The program generates the first 10 terms of the sequence. *) (* Harvey P. Dale, Sep 21 2022 *)
  • PARI
    is(n) = Mod(7, n)^n==-3 \\ Felix Fröhlich, Oct 14 2016

Formula

A066438(a(n)) = a(n) - 3 for n > 2.

Extensions

a(15)-a(20) 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

A333134 Positive integers k such that 11^k == 2 (mod k).

Original entry on oeis.org

1, 3, 413, 1329, 6587, 11629, 75761, 925071199, 9031140861789, 114876097917387, 1314252479257933
Offset: 1

Views

Author

Seiichi Manyama, Mar 20 2020

Keywords

Comments

No other terms below 10^16. Some larger terms: 1584680529929001639, 15598123298097725094806152851164088027801112472240274433891889912569153113. - Max Alekseyev, Jan 07 2025

Crossrefs

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=11), A116622 (b=13), A333269 (b=17).
Cf. A015960.

Programs

  • PARI
    for(k=1, 1e6, if(Mod(11, k)^k==2, print1(k", ")))

Extensions

a(9)-a(11) from Max Alekseyev, Jan 07 2025
Showing 1-7 of 7 results.

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