cp's OEIS Frontend

A269099 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.

%I A269099 #13 Mar 31 2016 13:22:24
%S A269099 5,10,13,16,20,25,31,32,33,37,40,41,43,44,47,51,54,63,64,70,71,72,73,
%T A269099 74,75,76,78,79,80,84,85,86,87,93,98,100,101,102,103,104,105,106,107,
%U A269099 108,109,110,111,112,113,115,126,129,130,132,133,134,135,136,137
%N A269099 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 A269099 Michel Lagneau, <a href="/A269099/b269099.txt">Table of n, a(n) for n = 1..5000</a>
%e A269099 5 is a member because we have:
%e A269099 prime(5 + 3) + prime(5 - 3) = 19 + 3 = 22;
%e A269099 prime(5 + 2) + prime(5 - 2) = 17 + 5 = 22.
%e A269099 10 is a member because we have:
%e A269099 prime(10 + 2) + prime(10 - 2) = 19 + 37 = 56;
%e A269099 prime(10 + 3) + prime(10 - 3) = 17 + 41 = 58;
%e A269099 prime(10 + 4) + prime(10 - 4) = 13 + 43 = 56;
%e A269099 prime(10 + 5) + prime(10 - 5) = 11 + 47 = 58;
%e A269099 prime(10 + 7) + prime(10 - 7) = 5 + 59 = 64;
%e A269099 prime(10 + 8) + prime(10 - 8) = 3 + 61 = 64;
%e A269099 and all the sums 56, 58 and 64 appear twice.
%p A269099 for n from 1 to 200 do:
%p A269099   lst:={}:W:=array(1..n-1):cr:=0:
%p A269099     for m from n-1 by -1 to 1 do:
%p A269099       q:=ithprime(n-m)+ithprime(n+m):lst:=lst union {q}:W[m]:=q:cr:=cr+1:
%p A269099     od:c:=0:
%p A269099 for k from 1 to cr do:
%p A269099 if W[k]=2*ithprime(n) then c:=c+1:
%p A269099   else fi:
%p A269099 od:
%p A269099 if c>1 then
%p A269099       printf(`%d, `,n):
%p A269099       else fi:
%p A269099   od :
%Y A269099 Cf. A269043.
%K A269099 nonn
%O A269099 1,1
%A A269099 _Michel Lagneau_, Feb 19 2016