A006307 Number of ways writing 2^n as unordered sums of 2 primes.

0, 0, 1, 1, 2, 2, 5, 3, 8, 11, 22, 25, 53, 76, 151, 244, 435, 749, 1314, 2367, 4239, 7471, 13705, 24928, 45746, 83467, 153850, 283746, 525236, 975685, 1817111, 3390038, 6341424, 11891654, 22336060, 42034097, 79287664, 149711134, 283277225, 536710100, 1018369893

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			n = 5: 2^5 = 32 = 3+29 = 13+19 so a(5) = 2.
		

References

• Bohman, Jan and Froberg, Carl-Erik; Numerical results on the Goldbach conjecture. Nordisk Tidskr. Informationsbehandling (BIT) 15 (1975), no. 3, 239-243.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A061358, A062602, A062610.

Programs

Maple

a:=proc(n) local c,k; c:=0: for k from 1 to floor((n-1)/2) do if isprime(2*k+1)=true and isprime(2*n-2*k-1)=true then c:=c+1 else c:=c fi od end: 0,0,1,seq(a(2*2^n),n=1..15); # Emeric Deutsch, Sep 22 2004

PARI

a(n)=my(N=2^n,s); forprime(q=2, N\2, s+=isprime(N-q)); s \\ Charles R Greathouse IV, Mar 02 2015

Formula

a(n) = A061358(2^n).

Extensions

More terms from David W. Wilson

a(28)-a(35) from Ray Chandler, Feb 21 2004

a(36)=79287664 and a(37)=149711134 from Ray Chandler, Apr 10 2005

a(38)-a(40) from Russ Cox, Nov 04 2006