%I
%S 2,3,5,7,23,37,53,101,103,131,149,151,167,181,229,257,263,277,293,311,
%T 359,373,389,421,439,487,503,599,613,631,641,643,647,661,677,727,743,
%U 757,769,773,821,823,853,887,919,983,997,1013,1031,1061,1063
%N Primes not expressed in form n<+>4, where operation <+> defined in A206853.
%C Or primes p such that, for any nonnegative integer n<p with the Hamming distance D(n,p)=4, there exists an integer m in the interval (n,p) with D(n,m)=4.
%t hammingDistance[a_, b_] := Count[IntegerDigits[BitXor[a, b], 2], 1]; (* binary Hamming distance *) vS[a_,b_] := NestWhile[#+1&, a, hammingDistance[a,#] =!= b&]; (* vS[a_,b_] is the least c>=a,such that the binary Hamming distance D(a,c)=b. vS[a,b] is Vladimir's a<+>b *) A210566 = Map[Prime[#]&, Complement[Range[Max[#]], #]&[Map[PrimePi[#]&, Union[Map[#[[2]]&, Cases[Map[{PrimeQ[#],#}&[vS[#,4]]&, Range[7000]],{True,_}]]]]]] (* _Peter J. C. Moses_, Apr 02 2012 *)
%Y Cf. A205509, A205510, A205511, A205302, A205649, A205533, A122565, A206852, A206853, A206960, A208982, A209544, A209554.
%K nonn,base
%O 1,1
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Mar 22 2012
