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%I M0344 #29 Dec 26 2021 21:32:37
%S 0,0,1,1,2,2,5,3,8,11,22,25,53,76,151,244,435,749,1314,2367,4239,7471,
%T 13705,24928,45746,83467,153850,283746,525236,975685,1817111,3390038,
%U 6341424,11891654,22336060,42034097,79287664,149711134,283277225,536710100,1018369893
%N Number of ways writing 2^n as unordered sums of 2 primes.
%D Bohman, Jan and Froberg, Carl-Erik; Numerical results on the Goldbach conjecture. Nordisk Tidskr. Informationsbehandling (BIT) 15 (1975), no. 3, 239-243.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%F a(n) = A061358(2^n).
%e n = 5: 2^5 = 32 = 3+29 = 13+19 so a(5) = 2.
%p 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
%o (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
%Y Cf. A061358, A062602, A062610.
%K nonn
%O 0,5
%A _N. J. A. Sloane_
%E More terms from _David W. Wilson_
%E a(28)-a(35) from _Ray Chandler_, Feb 21 2004
%E a(36)=79287664 and a(37)=149711134 from _Ray Chandler_, Apr 10 2005
%E a(38)-a(40) from _Russ Cox_, Nov 04 2006
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