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A210566 Primes not expressed in form n<+>4, where operation <+> defined in A206853. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A106711 A235110

Adjacent sequences:  A210563 A210564 A210565 * A210567 A210568 A210569

KEYWORD

nonn,base

AUTHOR

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

STATUS

approved

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Last modified November 16 22:05 EST 2019. Contains 329208 sequences. (Running on oeis4.)