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.

5, 10, 13, 16, 20, 25, 31, 32, 33, 37, 40, 41, 43, 44, 47, 51, 54, 63, 64, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 84, 85, 86, 87, 93, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 126, 129, 130, 132, 133, 134, 135, 136, 137

Offset: 1

Author

Michel Lagneau, Feb 19 2016

Keywords

• nonn

Examples

			5 is a member because we have:
prime(5 + 3) + prime(5 - 3) = 19 + 3 = 22;
prime(5 + 2) + prime(5 - 2) = 17 + 5 = 22.
10 is a member because we have:
prime(10 + 2) + prime(10 - 2) = 19 + 37 = 56;
prime(10 + 3) + prime(10 - 3) = 17 + 41 = 58;
prime(10 + 4) + prime(10 - 4) = 13 + 43 = 56;
prime(10 + 5) + prime(10 - 5) = 11 + 47 = 58;
prime(10 + 7) + prime(10 - 7) = 5 + 59 = 64;
prime(10 + 8) + prime(10 - 8) = 3 + 61 = 64;
and all the sums 56, 58 and 64 appear twice.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A269043.

Programs

Maple

for n from 1 to 200 do:
  lst:={}:W:=array(1..n-1):cr:=0:
    for m from n-1 by -1 to 1 do:
      q:=ithprime(n-m)+ithprime(n+m):lst:=lst union {q}:W[m]:=q:cr:=cr+1:
    od:c:=0:
for k from 1 to cr do:
if W[k]=2*ithprime(n) then c:=c+1:
  else fi:
od:
if c>1 then
      printf(`%d, `,n):
      else fi:
  od :