A215747 a(n) = (-2)^n mod n.

0, 0, 1, 0, 3, 4, 5, 0, 1, 4, 9, 4, 11, 4, 7, 0, 15, 10, 17, 16, 13, 4, 21, 16, 18, 4, 1, 16, 27, 4, 29, 0, 25, 4, 17, 28, 35, 4, 31, 16, 39, 22, 41, 16, 28, 4, 45, 16, 19, 24, 43, 16, 51, 28, 12, 32, 49, 4, 57, 16, 59, 4, 55, 0, 33, 64, 65, 16, 61, 44, 69, 64, 71, 4, 7

Offset: 1

Author

Alex Ratushnyak, Aug 23 2012

Keywords

• nonn
• look
• changed

Comments

n^(n+2) mod (n+2) is essentially the same.

Indices of 0's: 2^k - 1, k>=0.

Indices of 1's: A006521 except the first term.

Indices of 3's: A015940.

Indices of 5's: 7, 133, 1517, 11761, ...

a(A000040(n)) = A000040(n)-2 = A040976(n).

Examples

			a(5) = (-2)^5 mod 5 = -32 mod 5 = 3.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A015910, A082493, A082494, A110146, A213381.

Programs

Maple

a:= n-> (-2)&^n mod n:
seq(a(n), n=1..100);  # Alois P. Heinz, Apr 08 2015

Mathematica

a[n_]:=Mod[(-2)^n ,n]; Array[a,75] (* Stefano Spezia, Aug 25 2025 *)

Python

for n in range(1, 333):
    print((-2)**n % n, end=',')