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Numbers n with the property that if there is a number j with prime(n+i) + prime(n-i) = j for some i, then there are least two choices for i that give this value of j.
1

%I #13 Mar 31 2016 13:22:24

%S 5,10,13,16,20,25,31,32,33,37,40,41,43,44,47,51,54,63,64,70,71,72,73,

%T 74,75,76,78,79,80,84,85,86,87,93,98,100,101,102,103,104,105,106,107,

%U 108,109,110,111,112,113,115,126,129,130,132,133,134,135,136,137

%N Numbers n with the property that if there is a number j with prime(n+i) + prime(n-i) = j for some i, then there are least two choices for i that give this value of j.

%H Michel Lagneau, <a href="/A269099/b269099.txt">Table of n, a(n) for n = 1..5000</a>

%e 5 is a member because we have:

%e prime(5 + 3) + prime(5 - 3) = 19 + 3 = 22;

%e prime(5 + 2) + prime(5 - 2) = 17 + 5 = 22.

%e 10 is a member because we have:

%e prime(10 + 2) + prime(10 - 2) = 19 + 37 = 56;

%e prime(10 + 3) + prime(10 - 3) = 17 + 41 = 58;

%e prime(10 + 4) + prime(10 - 4) = 13 + 43 = 56;

%e prime(10 + 5) + prime(10 - 5) = 11 + 47 = 58;

%e prime(10 + 7) + prime(10 - 7) = 5 + 59 = 64;

%e prime(10 + 8) + prime(10 - 8) = 3 + 61 = 64;

%e and all the sums 56, 58 and 64 appear twice.

%p for n from 1 to 200 do:

%p lst:={}:W:=array(1..n-1):cr:=0:

%p for m from n-1 by -1 to 1 do:

%p q:=ithprime(n-m)+ithprime(n+m):lst:=lst union {q}:W[m]:=q:cr:=cr+1:

%p od:c:=0:

%p for k from 1 to cr do:

%p if W[k]=2*ithprime(n) then c:=c+1:

%p else fi:

%p od:

%p if c>1 then

%p printf(`%d, `,n):

%p else fi:

%p od :

%Y Cf. A269043.

%K nonn

%O 1,1

%A _Michel Lagneau_, Feb 19 2016