A121062 Partition numbers mod 4.

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, 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, 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

Offset

0,3

Comments

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

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

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

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

Links

Table of n, a(n) for n=0..104.

Formula

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

a(n) = A000025(n) mod 4. - John M. Campbell, Jun 29 2016

Mathematica

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

Prog

(PARI) a(n) = numbpart(n) % 4; \\ Michel Marcus, Jun 29 2016

Crossrefs

Cf. A000041, A010873, A049575.

Sequence in context: A080717 A239214 A200181 * A045831 A338988 A046821

Adjacent sequences: A121059 A121060 A121061 * A121063 A121064 A121065

Keyword

nonn,easy

Author

Jonathan Vos Post, Aug 10 2006

Extensions

More terms from Robert G. Wilson v, Aug 17 2006

Status

approved