A214844 Number of partitions of 2^n into three distinct primes.

0, 0, 0, 1, 3, 2, 10, 8, 32, 18, 75, 51, 292, 140, 518, 534, 2167, 1292, 6055, 4318, 23899, 16589, 53108, 46683, 312340, 159483, 567857, 639256, 2810965, 1826974

Offset: 1

Author

Zak Seidov, Mar 08 2013

Keywords

• nonn

Examples

			a(4) = 1 because 2^4 = 16 = 2 + 3 + 11 (1 partition),
a(5) = 3 because 2^5 = 32 = 2 + 7 + 23 = 2 + 11 + 19 = 2 + 13 + 17 (3 partitions).
		

Links

• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A125688.

Programs

Mathematica

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}]
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 *)

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

Formula

a(n) = A061357(2^(n-1) - 1) for n > 2. - Charles R Greathouse IV, Mar 08 2013