A006307 Number of ways writing 2^n as unordered sums of 2 primes. (Formerly M0344)

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

0,5

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

Table of n, a(n) for n=0..40.

Index entries for sequences related to Goldbach conjecture

Formula

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

Example

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

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

Prog

(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

Crossrefs

Cf. A061358, A062602, A062610.

Sequence in context: A071939 A338332 A075545 * A152991 A163298 A133440

Adjacent sequences: A006304 A006305 A006306 * A006308 A006309 A006310

Keyword

nonn

Author

N. J. A. Sloane

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

Status

approved