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 1-3 of 3 results.

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

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

Showing 1-3 of 3 results.

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