parity of integer sequences

[jeremy.gardiner at btinternet.com]

The following sequences all appear to have the same parity (with extra zero term at the start of A010051):

ID Number: A010051
Sequence:  0,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,
           0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,
           0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,1,0
Name:      Characteristic function of primes: 1 if n is prime else 0.

ID Number: A061007
Sequence:  0,1,1,2,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,
           1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,
           1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,
           0,0,0,0,0,0,1,0,0,0,1,0,1,0,0
Name:      -(n-1)! mod n.

ID Number: A035026
Sequence:  0,1,1,2,3,2,3,4,4,4,5,6,5,4,6,4,7,8,3,6,8,6,7,10,8,6,10,6,7,
           12,5,10,12,4,10,12,9,10,14,8,9,16,9,8,18,8,9,14,6,12,16,10,
           11,16,12,14,20,12,11,24,7,10,20,6,14,18,11,10,16,14,15,22,
           11,10,24,8,16,22,9,16,20,10
Name:      Number of times that i and 2n-i are both prime, for i=1,...2n-1.

ID Number: A069754
Sequence:  0,1,1,2,3,4,5,6,6,6,7,8,9,10,10,10,11,12,13,14,14,14,15,16,
           16,16,16,16,17,18,19,20,20,20,20,20,21,22,22,22,23,24,25,26,
           26,26,27,28,28,28,28,28,29,30,30,30,30,30,31,32,33,34,34,34,
           34,34,35,36,36,36,37,38,39
Name:      Counts transitions between prime and composite to reach the number n.

ID Number: A071574
Sequence:  0,1,3,2,7,6,5,4,14,12,15,10,13,8,28,24,11,30,9,20,26,16,29,
           56,48,22,60,18,25,40,31,52,32,58,112,96,21,44,120,36,27,50,
           17,80,62,104,57,64,116,224,192,42,49,88,240,72,54,100,23,34,
           61,160,124,208,114,128,19
Name:      If n = k-th prime, a(n)=2*a(k) 1; if n = k-th nonprime, a(n)=2*a(k).


Jeremy Gardiner