# Some sequences with the same parity

Jeremy Gardiner jeremy.gardiner at btinternet.com
Sun Mar 16 13:48:50 CET 2003

The following sequences in the OEIS all have the same parity;

A004737, A006590, A027052, A071028, A071797, A078358, A078446.

%S A004737 1,1,2,1,1,2,3,2,1,1,2,3,4,3,2,1,1,2,3,4,5,4,3,2,1,1,2,3,4,5
%N A004737 Concatenation of sequences (1,2,..,n-1,n,n-1,..,1) for n >= 1.

%S A006590 1,3,6,9,13,16,21,24,29,33,38,41,48,51,56,61,67,70,77,80,87
%N A006590 Sum_{k=1..n} ceiling(n/k)

%S A027052 1,1,0,1,1,0,1,2,1,1,0,1,2,3,4,1,1,0,1,2,3,6,9,8,1,1,0,1,2,3
%N A027052  Triangular array T by rows: T(n,0)=T(n,2n)=1 for n >= 0

%S A071028 1,1,0,1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1
%N A071028 Triangle giving successive states of cellular automaton generated
by "rule 50"

%S A071797 1,1,2,3,1,2,3,4,5,1,2,3,4,5,6,7,1,2,3,4,5,6,7,8,9,1,2,3,4,5
%N A071797 Restart counting after each new odd integer (a fractal sequence).

%S A078358 1,3,4,5,7,8,9,10,11,13,14,15,16,17,18,19,21,22,23,24,25,26
%N A078358 Complementary numbers to A002378.

%S A078446 1,1,2,3,1,4,5,2,7,1,8,9,4,13,2,15,1,16,17,8,25,4,29,2,31,1
%N A078446 a(1)=a(2)=1; a(n)=a(n-2)/2 if a(n-2) is even, a(n)=a(n-1)+a(n-2)
otherwise.

Jeremy Gardiner
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