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
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
LINKS
Eric Weisstein's World of Mathematics, Primorial.
FORMULA
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
KEYWORD
nonn,hard,more
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