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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 (list; graph; refs; listen; history; text; internal format)
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[2n-Prime[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

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Last modified June 24 22:23 EDT 2021. Contains 345445 sequences. (Running on oeis4.)