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 1-6 of 6 results.

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.

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

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

A333413 Positive integers k such that k divides 13^k + 2.

Original entry on oeis.org

1, 3, 5, 185, 2199, 14061, 5672119, 6719547, 192178873, 913591893, 4589621727, 9762178659, 1157052555699
Offset: 1

Views

Author

Seiichi Manyama, Mar 20 2020

Keywords

Comments

a(14) > 6*10^12. - Giovanni Resta, Mar 29 2020

Crossrefs

Solutions to 13^k == m (mod k): this sequence (m = -2), A015963 (m = -1), A116621 (m = 1), A116622 (m = 2), A116629 (m = 3), A116630 (m = 4), A116611 (m = 5), A116631 (m = 6), A116632 (m = 7), A295532 (m = 8), A116636 (m = 9), A116620 (m = 10), A116638 (m = 11), A116639 (k = 15).
Solutions to b^k == -2 (mod k): A015973 (b = 3), A123062 (b = 5), A277370 (b = 7), this sequence (b = 13), A333414 (b = 17).

Programs

  • Mathematica
    Select[Range[100000], Divisible[PowerMod[13, #, #] + 2, #] &] (* Jinyuan Wang, Mar 28 2020 *)
  • PARI
    for(k=1, 1e6, if(Mod(13, k)^k==-2, print1(k", ")))

Extensions

a(13) from Giovanni Resta, Mar 29 2020

A333414 Positive integers k such that k divides 17^k + 2.

Original entry on oeis.org

1, 19, 35, 115, 44095, 211117, 14376053, 43472060395, 561558718915, 2182879071661
Offset: 1

Views

Author

Seiichi Manyama, Mar 20 2020

Keywords

Comments

a(8) > 10^10.
a(11) > 4*10^12. - Giovanni Resta, Mar 22 2020

Crossrefs

Solutions to b^n == -2 (mod n): A015973 (b=3), A123062 (b=5), A277370 (b=7), A333413 (b=13), this sequence (b=17).
Cf. A333269.

Programs

  • PARI
    for(k=1, 1e6, if(Mod(17, k)^k==-2, print1(k", ")))

Extensions

a(8)-a(10) from Giovanni Resta, Mar 22 2020
Showing 1-6 of 6 results.

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