%I #14 Mar 08 2013 14:38:01
%S 0,0,0,1,3,2,10,8,32,18,75,51,292,140,518,534,2167,1292,6055,4318,
%T 23899,16589,53108,46683,312340,159483,567857,639256,2810965,1826974
%N Number of partitions of 2^n into three distinct primes.
%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%F a(n) = A061357(2^(n-1) - 1) for n > 2. - _Charles R Greathouse IV_, Mar 08 2013
%e a(4) = 1 because 2^4 = 16 = 2 + 3 + 11 (1 partition),
%e a(5) = 3 because 2^5 = 32 = 2 + 7 + 23 = 2 + 11 + 19 = 2 + 13 + 17 (3 partitions).
%t Do[Print[{k, n=2^k; s=0; Do[p=Prime[i]; Do[q=Prime[j]; r=n-p-q; If[r>q && PrimeQ[r], s++], {j, i+1, PrimePi[(n-p)/2]}], {i,1}]; s}], {k,30}]
%t Table[m = 2^n - 2; cnt = 0; p = 3; While[p < m/2, If[PrimeQ[m - p], cnt++]; p = NextPrime[p]]; cnt, {n, 20}] (* _T. D. Noe_, Mar 08 2013 *)
%o (PARI) a(n)=my(N=2^n-2,s);forprime(p=3,N/2-1,s+=ispseudoprime(N-p));s \\ _Charles R Greathouse IV_, Mar 08 2013
%Y Cf. A125688.
%K nonn
%O 1,5
%A _Zak Seidov_, Mar 08 2013