A242189 a(n) is the smallest prime number such that every number from 6 to 2n can be written as the sum of two primes less than or equal to a(n).

3, 5, 5, 7, 7, 11, 11, 13, 13, 13, 13, 17, 17, 19, 19, 19, 19, 23, 23, 31, 31, 31, 31, 31, 31, 37, 37, 37, 37, 41, 41, 41, 41, 41, 41, 47, 47, 47, 47, 47, 47, 47, 47, 61, 61, 61, 61, 61, 61, 61, 61, 61, 67, 67, 67, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 83

Offset

3,1

Comments

The two primes stated in the name can be equal.

Links

Lei Zhou, Table of n, a(n) for n = 3..5881

Example

n=3, 2*3=6=3+3. Since 3 is the smallest prime needed, a(3)=3.
n=4, 2*3=6=3+3, 2*4=8=5+3, Since 5 is the smallest prime needed, a(4)=5.
...
n=14, we need to consider the even numbers from 6 to 2*14=28, while trying to minimize the larger prime number used to decompose such even numbers. 6=3+3; 8=5+3; 10=5+5; 12=7+5; 14=7+7; 16=11+5; 18=11+7; 20=13+7; 22=11+11; 24=13+11; 26=13+13; 28=17+11. The maximum prime number used is 17. So a(14)=17.

Mathematica

a = {2}; Table[found = 0; While[la = Length[a]; xx = 1; Do[yy = 0; Do[If[MemberQ[a, i*2 - a[[j]]], yy = 1], {j, 1, la}]; If[yy == 0, xx = 0], {i, 3, n}]; If[xx == 1, found = 1]; found == 0, AppendTo[a, NextPrime[Last[a]]]]; Last[a], {n, 3, 68}]

Crossrefs

Cf. A000040, A002375, A240708, A237628, A237638.

Sequence in context: A112276 A079578 A066169 * A302756 A305216 A087821

Adjacent sequences: A242186 A242187 A242188 * A242190 A242191 A242192

Keyword

nonn

Author

Lei Zhou, May 06 2014

Status

approved