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.

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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

A292331 Numbers k such that k^2 divides 5^k + 1.

Original entry on oeis.org

1, 3, 21, 609, 903, 2667, 9429, 26187, 77343, 114681, 159663, 212541, 273441, 405447, 1197483, 1357503, 1398747, 3325749, 4451181, 4630227, 6099429, 6865509, 8620941, 9139263, 11757963, 13047447, 20277201, 26992707, 34727007, 37088709, 38596929, 39367587, 40563663, 51491769, 58372629, 59280123, 63002541, 71688687, 95430909
Offset: 1

Views

Author

Max Alekseyev, Sep 14 2017

Keywords

Links

Crossrefs

Subsequence of A015951.
Cf. A127105, A128679.

A292392 Numbers n such that n^2 divides (17^n + 1).

Original entry on oeis.org

1, 3, 9, 21, 39, 63, 117, 273, 819, 2067, 3081, 6201, 9243, 12807, 14469, 21567, 43407, 48711, 50877, 64701, 89649, 146133, 149331, 163293, 166491, 221169, 340977, 356139, 447993, 489879, 546819, 661401, 663507, 1022931, 1143051, 1165437, 1548183, 1639911, 1640457
Offset: 1

Views

Author

K. D. Bajpai, Sep 15 2017

Keywords

Comments

After a(1), all the terms are multiples of 3.
From Robert Israel, Sep 18 2017: (Start)
All terms are odd.
If m and n are terms then lcm(m,n) is a term.
If n is a term not divisible by 9, then 3n is a term. (End)

Examples

			3 appears is a term because 3^2 divides (17^3 + 1): 4914/9 = 546.
9 appears is a term because 9^2 divides (17^9 + 1): 118587876498/81 = 1464047858.

Crossrefs

Cf. A015951, A123047, A123052, A177813, A292331.

Programs

  • Maple
    A292392:= proc(n) if(17 &^ n+1)mod (n^2)=0  then RETURN (n); fi; end: seq(A292392(n), n=1..50000);
  • Mathematica
    Select[Range[50000], IntegerQ[(PowerMod[17, #, #^2] + 1)/#^2] &]
  • PARI
    for(n=1, 5e6, if (Mod(17, n^2)^n==-1, print1(n, ", ")));
  • PARI
    is(n) = Mod(17, n^2)^n==-1 \\ Felix Fröhlich, Sep 16 2017
Previous Showing 21-23 of 23 results.

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

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