%I A116979
%S A116979 0,0,1,3,19,114,905,9493,124180,2044847,43755729
%N A116979 Number of distinct representations of primorials as the sum of two primes.
%C A116979 Related to Goldbach's conjecture. Let g(2n)=A002375(n). The primorials 
               produce maximal values of the function g in the following sense: 
               the basic shape of the function g is k*x/log(x)^2 and each primorial 
               requires a larger value of k than the previous one. - T. D. Noe (noe(AT)sspectra.com), 
               Apr 28 2006
%H A116979 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Primorial.html">Primorial.</a>
%F A116979 a(n) = #{p(i) + p(j) = A002110(n) for p(k) = A000040(k) and i >= j}.
%e A116979 a(2) = 1 because 2nd primorial = 6 = 3 + 3 uniquely.
%e A116979 a(3) = 3 because 3rd primorial = 30 = 7 + 23 = 11 + 19 = 13 + 17.
%e A116979 a(4) = 19 because 4th primorial = 210 = 11 + 199 = 13 + 197 = 17 + 193 
               = 19 + 191 = 29 + 181 = 31 + 179 = 37 + 173 = 43 + 167 = 47 + 163 
               = 53 + 157 = 59 + 151 = 61 + 149 = 71 + 139 = 73 + 137 = 79 + 131 
               = 83 + 127 = 97 + 113 = 101 + 109 = 103 + 107.
%t A116979 n=1; Join[{0,0}, Table[n=n*Prime[k]; cnt=0; Do[If[PrimeQ[2n-Prime[i]],
               cnt++ ], {i,2,PrimePi[n]}]; cnt, {k,2,10}]] - T. D. Noe (noe(AT)sspectra.com), 
               Apr 28 2006
%Y A116979 Cf. A000040, A002110.
%Y A116979 Cf. A002375 (number of decompositions of 2n into unordered sums of two 
               odd primes).
%Y A116979 Sequence in context: A037154 A037774 A037662 this_sequence A037781 A037585 
               A084133
%Y A116979 Adjacent sequences: A116976 A116977 A116978 this_sequence A116980 A116981 
               A116982
%K A116979 nonn
%O A116979 0,4
%A A116979 Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 01 2006
%E A116979 More terms from T. D. Noe (noe(AT)sspectra.com), Apr 28 2006