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

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

1,3

Comments

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.

Links

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

Example

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

Maple

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

Mathematica

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

Crossrefs

Cf. A064935, A115976.

Sequence in context: A311652 A311653 A370596 * A171949 A217319 A133466

Adjacent sequences: A381119 A381120 A381121 * A381123 A381124 A381125

Keyword

nonn

Author

Robert Israel, Feb 14 2025

Status

approved