A171691 - OEIS

%I #6 Jan 05 2020 16:32:55

%S 1,1,0,1,1,1,1,2,2,3,1,3,2,3,3,5,2,5,3,5,4,6,3,7,5,7,5,8,5,9,6,8,7,10,

%T 7,12,7,9,9,12,8,13,9,12,10,13,9,15,11,15,11,15,11,17,13,16,13,17,13,

%U 20,14,16,15,20,15,22,15,18,17,22,16,23,17,21,18,23,18,26,18,23

%N Number of unordered partitions {k1, k2} of n such that k1 and k2 are nonnegative nonprimes A141468.

%H Andrew Howroyd, <a href="/A171691/b171691.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 1 because 1 = 0 + 1.

%e a(2) = 1 because 2 = 1 + 1.

%e a(3) = 0.

%e a(4) = 1 because 4 = 0 + 4.

%e a(5) = 1 because 5 = 1 + 4.

%e a(6) = 1 because 6 = 0 + 6.

%e a(7) = 1 because 7 = 1 + 6.

%e a(8) = 2 because 8 = 0 + 8 = 4 + 4.

%o (PARI) a(n)={sum(i=0, n\2, (i<2 || !isprime(i)) && !isprime(n-i))} \\ _Andrew Howroyd_, Jan 05 2020

%Y Cf. A062610, A141468, A224708.

%K nonn

%O 1,8

%A _Juri-Stepan Gerasimov_, Dec 15 2009

%E Name clarified and terms a(55) and beyond from _Andrew Howroyd_, Jan 05 2020