A210566 Primes not expressed in form n<+>4, where operation <+> defined in A206853.

2, 3, 5, 7, 23, 37, 53, 101, 103, 131, 149, 151, 167, 181, 229, 257, 263, 277, 293, 311, 359, 373, 389, 421, 439, 487, 503, 599, 613, 631, 641, 643, 647, 661, 677, 727, 743, 757, 769, 773, 821, 823, 853, 887, 919, 983, 997, 1013, 1031, 1061, 1063

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..51.

Mathematica

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 *)

Crossrefs

Cf. A205509, A205510, A205511, A205302, A205649, A205533, A122565, A206852, A206853, A206960, A208982, A209544, A209554.

Sequence in context: A284060 A211682 A100552 * A155873 A362678 A106711

Adjacent sequences: A210563 A210564 A210565 * A210567 A210568 A210569

Keyword

nonn,base

Author

Vladimir Shevelev and Peter J. C. Moses, Mar 22 2012

Status

approved