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Partition numbers mod 4.
0

%I #16 Jun 29 2016 11:39:14

%S 1,1,2,3,1,3,3,3,2,2,2,0,1,1,3,0,3,1,1,2,3,0,2,3,3,2,0,2,2,1,0,2,1,3,

%T 2,3,1,1,3,1,2,3,2,1,3,2,2,2,1,1,2,3,1,3,3,0,3,2,0,0,3,1,0,3,2,2,0,1,

%U 3,1,0,1,3,1,0,0,3,3,0,2,0,3,3,1,0,1,2,1,1,1,1,3,3,1,0,3,0,2,0,3,0,2,3,2,1

%N Partition numbers mod 4.

%C P_n==0: 11, 15, 21, 26, 30, 55, 58, 59, 62, 66, 70, 74, 75, 78, 80, 84, 94, 96, 98, 100, ... .

%C P_n==1: 0, 1, 4, 12, 13, 17, 18, 29, 32, 36, 37, 39, 43, 48, 49, 52, 61, 67, 69, 71, 73, ... .

%C P_n==2: 2, 8, 9, 10, 19, 22, 25, 27, 28, 31, 34, 40, 42, 45, 46, 47, 50, 57, 64, 65, 79, ... .

%C P_n==3: 3, 5, 6, 7, 14, 16, 20, 23, 24, 33, 35, 38, 41, 44, 51, 53, 54, 56, 60, 63, 68, ... .

%F a(n) = A000041(n) mod 4 = A010873(A000041(n)).

%F a(n) = A000025(n) mod 4. - _John M. Campbell_, Jun 29 2016

%t f[n_] := Mod[PartitionsP@n, 4]; Table[f@n, {n, 0, 104}] (* _Robert G. Wilson v_ *)

%o (PARI) a(n) = numbpart(n) % 4; \\ _Michel Marcus_, Jun 29 2016

%Y Cf. A000041, A010873, A049575.

%K nonn,easy

%O 0,3

%A _Jonathan Vos Post_, Aug 10 2006

%E More terms from _Robert G. Wilson v_, Aug 17 2006