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
Keywords
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
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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 :