This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A116979 #16 Feb 16 2025 08:33:00
%S A116979 0,0,1,3,19,114,905,9493,124180,2044847,43755729,1043468386,
%T A116979 30309948241
%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_, Apr 28 2006
%C A116979 Relates also to a more generic problem of how many numbers there are such that their arithmetic derivative is equal to the n-th primorial number. See A351029. - _Antti Karttunen_, Jan 17 2024
%H A116979 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Primorial.html">Primorial.</a>
%H A116979 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%F A116979 a(n) = #{p(i) + p(j) = A002110(n) for p(k) = A000040(k) and i >= j}.
%F A116979 a(n) = A351029(n) - A369000(n). - _Antti Karttunen_, Jan 17 2024
%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_, Apr 28 2006 *)
%Y A116979 Cf. A000040, A002110, A351029, A369000.
%Y A116979 Cf. A002375 (number of decompositions of 2n into unordered sums of two odd primes).
%K A116979 nonn,hard,more
%O A116979 0,4
%A A116979 _Jonathan Vos Post_, Apr 01 2006
%E A116979 More terms from _T. D. Noe_, Apr 28 2006
%E A116979 a(11)-a(12) from _Donovan Johnson_, Dec 19 2009