%I #25 Jan 12 2023 01:38:36

%S 1,2,0,3,4,4,0,2,6,6,4,7,8,2,0,9,16,10,4,2,12,12,16,8,14,20,4,15,16,

%T 16,0,2,18,22,16,19,20,2,24,21,16,22,4,38,24,24,16,32,6,2,4,27,34,52,

%U 8,2,30,30,4,31,32,2,0,8,16,34,4,2,46,36,16,37,38,17

%N a(n) = 2^n mod (n+2).

%C Conjectures:

%C 1. Indices of zeros: 2^(x+2)-2, x >= 0.

%C 2. There are infinitely many n's such that a(n)=n.

%C 3. Every integer k >= 0 appears in a(n) at least once.

%C 4. Every k >= 0 appears in a(n) infinitely many times.

%H G. C. Greubel, <a href="/A213859/b213859.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = 2^n mod (n+2).

%F a(n) = A106262(2*n, n). - _G. C. Greubel_, Jan 11 2023

%t Table[PowerMod[2, n, n+2], {n, 0, 100}] (* _T. D. Noe_, Jun 26 2012 *)

%o (Python)

%o print([2**n % (n+2) for n in range(222)])

%o (Magma) [Modexp(2,n,n+2): n in [0..120]]; // _G. C. Greubel_, Jan 11 2023

%o (SageMath) [power_mod(2,n,n+2) for n in range(121)] # _G. C. Greubel_, Jan 11 2023

%Y Cf. A015910, A066606, A062173, A106262.

%K nonn,easy

%O 0,2

%A _Alex Ratushnyak_, Jun 22 2012