

A297929


Lexicograpically earliest sequence of distinct prime numbers such that for any n > 1, a(n) is at Hamming distance one from some previous term.


1



2, 3, 7, 5, 11, 13, 19, 17, 23, 29, 31, 37, 43, 41, 47, 53, 59, 61, 67, 71, 79, 83, 101, 97, 103, 107, 109, 113, 131, 139, 137, 151, 149, 157, 163, 167, 179, 181, 199, 197, 193, 211, 227, 229, 241, 263, 269, 271, 293, 317, 313, 281, 283, 347, 331, 353, 359
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OFFSET

1,1


COMMENTS

For any n > 1, a(n) = a(m) XOR 2^k for some m < n and k >= 0 (where XOR denotes the bitwise XOR operator).
This sequence was inspired by A294994.
Let define the binary relation R over prime numbers as follows:
 for any prime numbers p and q, p is Rrelated to q iff there exists a finite list of prime numbers, say (c(1), ..., c(k)), such that c(1) = p and c(k) = q and A000120(c(i) XOR c(i+1)) = 1 for i = 1..k1,
 R is a equivalence relation,
 this sequence corresponds to the Requivalence class of the prime number 2.
Is this sequence infinite?
Will every prime number appear?


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Scatterplot of the first 359854 terms (a(359855) is the first term > 2^23)
Rémy Sigrist, Illustration of the first terms
Rémy Sigrist, PARI program for A297929


EXAMPLE

See illustration of the first terms in Links section.


MATHEMATICA

With[{nn = 56}, Nest[Function[a, Append[a, SelectFirst[Prime@ Range[3 nn/2], Function[p, And[FreeQ[a, p], AnyTrue[a, Total@ IntegerDigits[BitXor[p, #], 2] == 1 &]]]]]], {2}, nn]] (* Michael De Vlieger, Jan 14 2018 *)


PROG

(PARI) See Links section.


CROSSREFS

Cf. A000120, A294994.
Sequence in context: A275205 A171039 A063904 * A221858 A139317 A117928
Adjacent sequences: A297926 A297927 A297928 * A297930 A297931 A297932


KEYWORD

nonn,base


AUTHOR

Rémy Sigrist, Jan 08 2018


STATUS

approved



