A205668 Prime numbers that cannot be expressed as the sum of two lesser primes of twin prime pairs + 1 or two greater primes of twin prime pairs - 1.
2, 3, 5, 97, 401, 787, 907, 1117
Offset: 1
Keywords
Examples
97 is here because neither 96 or 98 is the sum of two primes from the set {2, 3, 5, 7, 11, 13, 17, 19, 29, 31, 41, 43, 59, 61, 71, 73}, which are the twin primes less than 100. - _T. D. Noe_, Feb 12 2012
Programs
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Mathematica
k=Insert[Select[Prime[Range[2,10^4]], PrimeQ[#-2]||PrimeQ[#+2]&], 5, 3]; u=Length@k/2; Complement[Prime[Range[4,10^4]], Select[Flatten[Join[Table[k[[2n-1]] + k[[2m-1]] + 1,{n,u}, {m,n}], Table[k[[2n]] + k[[2m]] - 1,{n,u}, {m,n}]]], PrimeQ]] -
PARI
lower=List();p=2;forprime(q=3,1e8,if(q-p==2,listput(lower,p));p=q) isk(n)=for(i=1,#lower,if(setsearch(lower,n-lower[i]),return(lower[i]));if(2*lower[i]>n,return(0)));error("ran out") is(n)=!isk(n-1)&&!isk(n-3) \\ Charles R Greathouse IV, Jan 31 2012
Comments