A115976 -id:A115976 - cp's OEIS frontend

A244673 Numbers k that divide 2^k + 4.

1, 2, 3, 4, 20, 260, 740, 2132, 2180, 5252, 43364, 49268, 49737, 80660, 130052, 293620, 542852, 661412, 717027, 865460, 1564180, 2185220, 2192132, 2816372, 3784916, 4377620, 4427540, 5722004, 6307652, 6919460, 8765252, 9084452, 9498260, 9723611, 11346260, 12208820, 12220132

Offset: 1

Derek Orr, Jul 14 2014

nonn

			2^2 + 4 = 8 is divisible by 2. Thus 2 is a term of this sequence.
2^3 + 4 = 12 is divisible by 3. Thus 3 is a term of this sequence.
2^4 + 4 = 20 is divisible by 4. Thus 4 is a term of this sequence.

Jens Kruse Andersen, Table of n, a(n) for n = 1..100
OEIS Wiki, 2^n mod n

The odd terms form A115976.

Cf. A015921, A140504.

A244673:=n->`if`(type((2^n+4)/n, integer), n, NULL): seq(A244673(n), n=1..10^5); # Wesley Ivan Hurt, Jul 15 2014
Alternative:
select(n -> 4 + 2&^n mod n = 0, [$1..10^5]); # Robert Israel, Jul 15 2014

Select[Range[1000], Mod[2^# + 4, #] == 0 &] (* Alonso del Arte, Jul 14 2014 *)
Join[{1,2,3},Select[Range[1223*10^4],PowerMod[2,#,#]==#-4&]] (* Harvey P. Dale, Jan 16 2023 *)

for(n=1, 10^8, if(Mod(2,n)^n+4==0, print1(n, ", "))) \\ Jens Kruse Andersen, Jul 15 2014

A357125 Positive integers n such that 2^(n-3) == -1 (mod n).

Original entry on oeis.org

1, 5, 4553, 46777, 82505, 4290773, 4492205, 4976429, 21537833, 21549349, 51127261, 56786089, 60296573, 80837773, 87761789, 94424465, 138644873, 168865001, 221395541, 255881453, 297460453, 305198249, 360306365, 562654205, 635374253, 673867253, 808333573, 1164757553, 1210317349

Offset: 1

Max Alekseyev, Sep 13 2022

nonn

Also, odd integers n dividing 2^n + 8.

Some large terms: 5603900696716667005, 446661376165868432471569407934747098747181600670953926245, 1533278864164902082788937853692280620552397221686019535813.

Max Alekseyev, Table of n, a(n) for n = 1..781 (all terms below 10^15)

The odd terms of A245319.

Cf. A006521, A115976, A276967, A251603.

Select[Range[2155*10^4],PowerMod[2,#-3,#]==#-1&]//Quiet (* The program generates the first 10 terms of the sequence. *) (* Harvey P. Dale, Feb 08 2025 *)

A381122 Numbers k such that k^(k+1) == k (mod k+2).

Original entry on oeis.org

0, 1, 4, 8, 12, 20, 24, 28, 32, 36, 44, 56, 60, 72, 80, 84, 92, 104, 116, 120, 132, 140, 144, 156, 164, 168, 176, 180, 192, 200, 204, 212, 216, 224, 252, 260, 272, 276, 296, 300, 312, 324, 332, 344, 356, 360, 380, 384, 392, 396, 420, 444, 452, 456, 464, 476, 480, 500, 512, 524, 536, 540, 552, 560

Offset: 1

Robert Israel, Feb 14 2025

nonn

Numbers k such that (-2)^(k+1) == k (mod k+2).
Odd terms are k-2 for k >= 3 in A115976.
Even terms are divisible by 4.

			a(5) = 12 is a term because 12^13 == 12 (mod 14).

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A064935, A115976.

select(k -> (-2) &^(k+1) mod (k+2) = k, [$1..1000]);

Select[Range[0,560],PowerMod[#,#+1,#+2]==#&] (* James C. McMahon, Feb 15 2025 *)

cp's OEIS Frontend

A244673 Numbers k that divide 2^k + 4.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

A357125 Positive integers n such that 2^(n-3) == -1 (mod n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A381122 Numbers k such that k^(k+1) == k (mod k+2).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica