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%I #19 Feb 13 2015 00:25:41
%S 0,0,2,61,899,11219,126905,1374229,14529946,151426672,1563147978,
%T 16031036348
%N Number of partitions of 10^n into 2 composite relatively prime parts.
%e a(2)=2 because 10^2 = 9 + 91 = 49 + 51, 9 and 91 are composite and coprime, 49 and 51 are composite and coprime.
%t a[n_] := Module[{cnt=0}, Do[If[!PrimeQ[k]&&!PrimeQ[10^n-k]&&GCD[k,10^n-k]==1,cnt++],{k,3,(1/2)10^n,2}]; cnt]
%o (PARI) a(n) = my(N=10^n, s=0); forstep(k=9, N/2, [2,2,4,2], s += !isprime(k) & !isprime(N-k)); s \\ _Charles R Greathouse IV_, May 17 2011
%o (PARI) a(n)=my(N=10^n,s=0,p=7);forprime(q=11,N/2,forstep(k=p+2,q-2,2,s+=k%5&!isprime(N-k));p=q);s+sum(k=precprime(N/2)+2,N/2,gcd(k,10)==1&!isprime(N-k)) \\ _Charles R Greathouse IV_, May 17 2011
%Y Cf. A000041, A023022, A000837.
%K nonn
%O 0,3
%A _Zak Seidov_, May 17 2011
%E a(9)-a(10) from _Charles R Greathouse IV_, May 18 2011
%E a(11) from _Charles R Greathouse IV_, May 20 2011
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