

A116979


Number of distinct representations of primorials as the sum of two primes.


5



0, 0, 1, 3, 19, 114, 905, 9493, 124180, 2044847, 43755729, 1043468386, 30309948241
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OFFSET

0,4


COMMENTS

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


LINKS

Table of n, a(n) for n=0..12.
Eric Weisstein's World of Mathematics, Primorial.
Index entries for sequences related to Goldbach conjecture


FORMULA

a(n) = #{p(i) + p(j) = A002110(n) for p(k) = A000040(k) and i >= j}.


EXAMPLE

a(2) = 1 because 2nd primorial = 6 = 3 + 3 uniquely.
a(3) = 3 because 3rd primorial = 30 = 7 + 23 = 11 + 19 = 13 + 17.
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.


MATHEMATICA

n=1; Join[{0, 0}, Table[n=n*Prime[k]; cnt=0; Do[If[PrimeQ[2nPrime[i]], cnt++ ], {i, 2, PrimePi[n]}]; cnt, {k, 2, 10}]] (* T. D. Noe, Apr 28 2006 *)


CROSSREFS

Cf. A000040, A002110.
Cf. A002375 (number of decompositions of 2n into unordered sums of two odd primes).
Sequence in context: A037154 A037774 A037662 * A267802 A229928 A309183
Adjacent sequences: A116976 A116977 A116978 * A116980 A116981 A116982


KEYWORD

nonn


AUTHOR

Jonathan Vos Post, Apr 01 2006


EXTENSIONS

More terms from T. D. Noe, Apr 28 2006
a(11)a(12) from Donovan Johnson, Dec 19 2009


STATUS

approved



